StartLayout 1st row StartRoot StartFraction 250 c cubed Over 9 d Superscript 6 Baseline EndFraction EndRoot space c greater-than-or-equal-to 0 and d greater-than-or-equal-to 0. 2nd row = StartRoot StartFraction 25 times 10 c squared times c Over 9 d Superscript 6 Baseline EndFraction EndRoot. 3rd Row = StartFraction StartRoot 25 EndRoot times StartRoot c squared EndRoot times StartRoot 10 c EndRoot Over StartRoot 9 d Superscript 6 Baseline EndRoot EndFraction EndLayout
Based on the work shown on the left, what is the simplest form of StartRoot StartFraction 250 c cubed Over 9 d Superscript 6 Baseline EndFraction EndRoot ?
The simplest form of the given algebraic expression √(250c³/9d⁶) is; 5c * (√10c)]/3d³
How to simplify algebra problems?We are given the algebra problems as;
√(250c³/9d⁶)
Now 250c³ can be broken down into 250 = 25c² × 10c
Thus, we now have;
√(250c³/9d⁶) = [√(25c²) * (√10c)]/√9d⁶
When we breakdown the above expression, we have;
5c * (√10c)]/3d³
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Answer:
the answer is a
Step-by-step explanation:
i got it right
Triangle WXY has the interior and exterior angles shown below.
Triangle X W Y. Angle W is (2 x minus 13) degrees and angle Y is x degrees. The exterior angle to angle X is 122 degrees.
What is Measure of angle W?
45 degrees
58 degrees
68 degrees
77 degrees
The correct option is last one 77 degrees.
Therefore the measure angle W is 77 degrees.
Step-by-step explanation:
Given:
Exterior angle = 122°
∠W = (2x-13)°
∠Y= x°
To Find:
∠W = (2x-13)° = ?
Solution:
Exterior Angle Property:
An exterior angle of a triangle is equal to the sum of the opposite interior angles.
Angle W and Angle Y are the interior angles of Exterior angle 122°.
∴
Substituting the values we get
Now Substitute 'x' in angle W we get
Therefore the measure angle W is 77 degrees.
Step-by-step explanation:
Find the condition of the expression:√3-2x-x^2
Answer:
-1 <= x <= 1
Step-by-step explanation:
√((1-2x+x^2)+2-2x^2)
= √((1-x)^2 + 2*(1-x)(1+x) )
điều kiện là 1 - x > =0 và 1+x >=0
giải 2 bất phương trình trên ta thu đc kết ququả
Sean used cross multiplication to correctly solve a rational equation. he found one valid solution and one extraneous solution. if 1 is the extraneous solution, which equation could he have solved?
The equation which he have solved is [tex]10/x^{2} -1=15/3x-3[/tex] as in this 1 is the extraneous solution.
Given four equations in which first equation is [tex]10/x^{2} -1=15/3x-3[/tex],second is (x+2)/(x+3)=6x/8, third is (4x-4)/(x+6)=x-1/10, fourth is 4/x-1=x+2/10.
We have to find such a equation which have a valid solution and one extraneous solution.
We have to solve these equation:
[tex]10/x^{2} -1=15/3x-3[/tex]
The above exprssion is not defined for x=1 so 1 is an extraneous solution. Simplifying the above equation by doing cross multiplication.
10(3x-3)=15([tex]x^{2} -1[/tex])
30(x-1)=15(x-1)(x+1) [We know that [tex]A^{2} -B^{2} =(A+B)(A-B)[/tex]
2=x+1
x=1
In the given equation 1 makes the denominator zero and 1 is the solution of the equation derived from cross multiplication.
Hence the correct equation which Sean solves is option A which is [tex]10/x^{2} -1=15/3x-3[/tex].
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The given question is incomplete as it should include the given figure.
Answer:see photo #15
Step-by-step explanation:
Use the properties of 30-60-90 and 45-45-90 triangles to solve for x in each of the problems below. Then decode the secret message by matching the answer with the corresponding letter/symbol from the exercises.
These problems are solved using the trigonometric function. Trigonometric functions provides the ratio of different sides of a right-angle triangle.
What are Trigonometric functions?The trigonometric function refer to function that are periodic in nature and which lend insight to the relationship between angles and the sides of a triangle that is right angled.
The solutions to x in the respective problems is given as follows:
1st.) x = 5 /Sin(30°)
x = 10
!) sin(45°) = 4/x
x = 4/sin(45°)
x = 4√2
I) Cos(45°) = √3 / x
x = √3 / Cos(45°)
x = √6
E) Tan(60°)
= (3√3) / x
x = (3√3) / 3
W) It is to be noted that for right-triangle that is isosceles in nature, the angle made by the legs and the hypotenuse is always 45°.
x = 45°
N) x² + x² = (7√2)²
x = 7
V) Tan(60°) = 7 / x
x = 7√3/3
K) x² + x² = (9)²
x = 9/√2
Y) Sin(60°) = 7√3/x
x = 14
M) Sin(30°) = x/11
x = 11/2
T) Sin(45°) = x/√10
x = √5
A) x + 2x + 90° = 180°
x = 30°
O) Sin(45°) = √2 / x
x = 2
R) Tan(30°) = x / 4
x = 4/√3
= 4√3 / 3
S) Sin(60°) = x / (10/3)
x = (5√3) / 3
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3. Donnell is doing market research for a major brand by surveying customers at a local mall.
The probability of a customer agreeing to take the survey is 22%. What is the probability that
one of the first five customers agrees to take the survey?
29%
54%
071%
74%
71% is the required probability here.
What is a probability simple definition?
A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
The probability serves as a gauge for the possibility that an event will occur. and a The probability equation is stated by the following notation: P(E) = Number of Favorable Outcomes/Number of Total Outcomes.
The number of customers out of 5 who agree to take the survey here could be modelled as a binomial distribution given as
x ` Bin (n = 5 , p = 0.22 )
Thus the probability here is computed as
P(X≥ 1) = 1 - P(X = 0) = 1 - (1 - 0.22)⁵
= 0.71 %
Therefore 71% is the required probability here.
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Write an equation of the line that passes through a pair of points: on a coordinate plane, a line goes through (0, 2) and (2, 0). a. y = x + 3 c. y = -x + 2 b. y = x - 3 d. y = -x - 2 please select the best answer from the choices provided a b c d
Since the y-intercept b = 2, hence the equation of the line will be y = -x +2
Equation of a lineThe formula for calculating the slope of a line is expressed as:
Slope = y2-y1/x2-x1
Given the coordinate points (0, 2) and (2, 0)
Slope = 0-2/2-0
Slope = -1
Since the y-intercept b = 2, hence the equation of the line will be y = -x +2
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Answer:
c
Step-by-step explanation:
This container is composed of a right circular cylinder and a right circular cone.
k
Which is closest to the surface area of the container?
C
1243 ft²
1696 ft²
754 ft²
490 ft²
24 ft-
13 ft
10 ft
The closest surface area of the container is: 1,696 ft².
What is the Volume of a Cone and a Cylinder?Curved surface area of a cone = πrl
Surface of a cylinder = 2πr(h + r)
Surface area of the container = Curved surface area of a cone + Surface of a cylinder - area of circular base
= πrl + 2πr(h + r) - πr²
r = 24/2 = 12 ft
l = 13 ft
h = 10 ft
Plug in the values
Surface area of the container = π(12)(13) + 2π×12(10 + 12) - π(12²) = 1,696.5 ft².
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Mark is investing his money. he thinks that he should make $10 for every $100 he invests. how much does he expect to make on an investment of $500?
Identify the slope and y-intercept of the line whose equation is given. write the y-intercept as an ordered pair. y = negative 2 x + 5 a. slope = negative 2; y-intercept (0, 5) b. slope = 2; y-intercept (0, 5) c. slope = 5; y-intercept (0, 2) d. slope = negative 5; y-intercept (0, 2) please select the best answer from the choices provided a b c d
The line having the equation, y = -2x + 5, has a slope = -2, and y-intercept = (0, 5). Thus, option A is the best choice.
The slope of a line is the tangent of the angle that the line makes with the positive side of the x-axis.
The y-intercept of a line is the point at which the line intersects the y-axis.
The standard form of a line is y = mx + b, where m represents the slope of the line, and b represents its y-intercept.
In the question, we are asked to identify the slope and the y-intercept of the line whose equation is y = -2x + 5.
Comparing the given equation of the line, y = -2x + 5, with the standard equation of a line, y = mx + b, we can say that,
m = -2, and b = 5.
Representing b as an ordered pair, we get (0, 5), as b represents the y-intercept which is a point on the y-axis, where the x-coordinate is always equal to zero.
Thus, we get the slope = -2, and the y-intercept = (0, 5).
The option representing the answer is option A.
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The length of the hypotenuse of a right triangle is 7 feet, and the length of one leg is 4 feet. what is the length of the other leg to the nearest tenth of a foot
The length of the other leg to the nearest tenth of a foot is 5.7 feet.
What is Pythagorean theorem?
A theorem in geometry: the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides.The Pythagoras theorem equation is expressed as, [tex]c^{2} = a^{2} + b^{2}[/tex], where 'c' = hypotenuse of the right triangle and 'a' and 'b' are the other two legs.We can use the Pythagorean Theorem to find the length of the other leg
[tex]a^{2} + b^{2} = c^{2}[/tex]
"a" and "c" represent the two legs of the triangle and "b" represents the perpendicular.
So,
[tex]b^{2} = c^{2} - a^{2}[/tex]
= 7² - 4²
b = [tex]\sqrt{49 - 16}[/tex]
[tex]b = \sqrt{33}[/tex] ⇒ 5.7 feet
Therefore, the length of the other leg to the nearest tenth of a foot is 5.7 feet.
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Suppose a and b are real numbers such that 17^a=16 and 17^b=4. What is 1/(2^a-b) ?
Since
[tex]17^a = 16 = 4^2 \implies 17^{a/2} = 4[/tex]
it follows that
[tex]17^b = 4 \implies 17^{a/2} = 17^b \implies \dfrac a2 = b \implies a = 2b[/tex]
Then
[tex]2^{a - b} = 2^{2b - b} = 2^b[/tex]
so that
[tex]\dfrac1{2^{a-b}} = 2^{-b}[/tex]
We also have
[tex]17^b = 4 \implies b = \log_{17}(4)[/tex]
so we can go on to say
[tex]\dfrac1{2^{a-b}} = \boxed{2^{-\log_{17}(4)}}[/tex]
which of these ratios are equivalent ratio
1:4 2:8 3:6 7:28
Answer:
1:4
2:8
7:28
Step-by-step explanation:
1:42:8 , 1:47:28, 1:4In the given figure, ΔABC is a right triangle.
The figure shows the right-angle triangle ABC. B is the length of AC and a is the height of BC and c is the base of AB.
What is true about ΔABC?
A.
sin(A) = cos(C) and cos(A) = sin(C)
B.
sin(A) = sin(C) and cos(A) = cos(C)
C.
sin(A) = cos(A) and sin(C) = cos(C)
D.
sin(A) = cos(C) and cos(A) = cos(C)
The true statement about right-angle triangle ABC is that: A. sin(A) = cos(C) and cos(A) = sin(C).
How to apply basic trigonometry?In order to determine the angles, we would apply basic trigonometry. From the diagram of the right-angled triangle shown below, we can deduce the following parameters:
Angle (θ) = 45°.Opposite (Opp) side = a.Hypotenuse (Hyp) = c.Adjacent (Adj) side = b.By applying the basic trigonometry functions, we have:
sin(A) = Opp/Hyp = a/c.
sin(C) = Opp/Hyp = c/b.
cos(A) = Adj/Hyp = c/b.
cos(C) = Adj/Hyp = a/c.
From the above, we can logically deduce that sin(A) is equal to cos(C) and cos(A) is equal to sin(C).
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Answer:
Step-by-step explanation:
The true statement about right-angle triangle ABC is that: A. sin(A) = cos(C) and cos(A) = sin(C).
How to apply basic trigonometry?
In order to determine the angles, we would apply basic trigonometry. From the diagram of the right-angled triangle shown below, we can deduce the following parameters:
Angle (θ) = 45°.
Opposite (Opp) side = a.
Hypotenuse (Hyp) = c.
Adjacent (Adj) side = b.
By applying the basic trigonometry functions, we have:
sin(A) = Opp/Hyp = a/c.
sin(C) = Opp/Hyp = c/b.
cos(A) = Adj/Hyp = c/b.
cos(C) = Adj/Hyp = a/c.
From the above, we can logically deduce that sin(A) is equal to cos(C) and cos(A) is equal to sin(C).
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two numbers that equal -8 when multiplying but thoses two numbers also have to equal to -7 when adding
Answer:
-8 and 1
Step-by-step explanation:
-8 x 1 is -8
-8+1 is -7
The time that passes between the time you see lightning and you hear the thunder depends on your distance from the lightning. With each km from the lightning 3 seconds pass.
a) Make a table of values for distances from 0 to 5 km.
b) Graph this relation. State whether it is a linear or non-linear relation.
c) Using your graphed relation, how much time passes before you hear lightning that occurs 4.5 km away?
d) Using your graphed relation, how far away are you if you hear the thunder in 1.5 seconds?
When the lightning occurs 4.5 km away then we will hear after 13.5 seconds and if we hear after 1.5 seconds then we are 0.5 km away from lightning.
Given With each km from the lightning 3 seconds passes.
a) The table of values for distances from 0 to 5 km.
Distances Time
0 0
1 3
2 6
3 9
4 12
5 15
b) The graph of lightning is a linear relation because it is increasing constantly by 3 seconds. f(x)=3x
c) When distance =1 , the time be 3 seconds
when distance =4.5 , the time=3*4.5
=13.5 seconds.
d) When time is 3 seconds = 1km
when time =1.5 seconds , the distance be 1/2=0.5 km.
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f(x) = ^3√4x
g(x) = 3x + 5
Find (f/g)(x). Include any restrictions on the domain.
The required function (f/g)(x) is 3√4x/2x+3 where x ≠ -3/2
How to Simplify Algebraic Functions?Given the functions;
f(x) = ∛4x
g(x) = 2x + 3
We want to find the resulting function (f/g)(x);
(f/g)(x) = f(x)/g(x)
Thus, (f/g)(x) = ∛4x/(2x + 3)
Restriction to the function occurs at the point where the denominator is equal to zero.
Thus;
2x + 3 = 0
2x = -3
x = -3/2
Thus, the required function (f/g)(x) is 3√4x/2x+3 where x ≠ -3/2
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A newspaper article about the results of a poll states: "In theory, the results of such a poll, in 99 cases out of 100 should differ by no more than 5 percentage points in either direction from what would have been obtained by interviewing all voters in the United States." Find the sample size suggested by this statement.
Group of answer choices
27
664
544
385
The sample size suggested by this statement is 664 option second is correct.
What is the margin of error(MOE)?It is defined as an error that provides an estimate of the percentage of errors in real statistical data.
The formula for finding the MOE:
[tex]\rm MOE = Z\times \dfrac{s}{\sqrt{n}}[/tex]
Where Z is the z-score at the confidence interval
s is the standard deviation
n is the number of samples.
At 99% confidence Z = 2.576
By using the MOE formula:
0.05 = 2.376×√(0.5(0.5)/n)
After calculating
n = 663.57 ≈ 664
Thus, the sample size suggested by this statement is 664 option second is correct.
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Mercedes receives a $25 gift card for downloading music and wants to determine how many songs she can purchase. each downloaded song costs $1.29. write and solve an inequality to determine m, the number of songs mercedes can purchase. what is the approximate solution to the inequality? round to the nearest whole number.
The solution to the inequality: [tex]1.29m\leq 25[/tex] is m=19.
What is inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Value of gift card=$25
Cost of each song=$1.29
Let m be the number of songs purchased.
Then, the required inequality is as follows:
[tex]1.29m\leq 25\\m\leq \frac{25}{1.29}\\ m\leq 19.38[/tex]
The value of m rounded to the nearest whole number is 19.
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Which of the following number lines represents the solution set of x/-1 >or= -4?
The number line that shows that x ≥ -4 is; Option B
How to Interpret Number Lines?
We want to find the number line that represents x ≥ -4
Now, for greater than sign, the number line would point to the right while for less than sign the number line would point to the left.
Now, for greater than or equal to sign the dot would be shaded and as such looking at the correct number line would be that in Option B.
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What is the difference between the sum of the first 2003 even counting numbers and the sum of the first 2003 odd counting numbers
The difference is 2003.
The formula for the sum of the first n even numbers is SE = n^{2} + n, (E standing for even).
The sum of the first n odd numbers is SO = n^{2}, (O standing for odd).
Knowing this, plug 2003 for n,
SE - SO= (2003^{2} + 2003) - (2003^{2}) = 2003
The difference is 2003.
A number that can be divided into two halves, i.e. into two equal parts is called an even number. Even numbers are exactly divisible by 2 which means the remainder will be 0.
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Beth wanted to buy vegetables. She noticed that brand A of black beans was on sale for 4 cans for 87 cents. Brand B was 3 cans for 79 cents. Which was a better buy?
Answer:
Brand A
Step-by-step explanation:
If you divide both brands to find how much one can costs, brand B costs more per can.
79 ÷ 3 = 26.34
87 ÷ 4 = 21.75
That being said, if brand B were to sell 4 cans instead of 3 it would be more than brand A's 4 cans. Brand A is cheaper than brand B would be.
The function f(x) is given by the set of ordered pairs.
The equation that is true and one that matches the set of ordered pairs of functions is option C. f (0) = 6
What is the equation about?Note that a function can be made to be a given set of ordered pairs such as the ordered pairs (2,4), (3,5), (4,6) can have input functions of (as domain) 2,3,4 and output functions of (as range) of 4,5,6.
So when you see the ordered pairs. {(1,0), (–10,2), (0,6), (3,17), (–2, –1)} one can see that the option that matches to the set of ordered pairs of functions above is f (0) = 6 value x = 0, f (x) = y = 6, ordered pairs (0.6)
See full question below
The function f (x) is given by the set of ordered pairs. {(1,0), (–10,2), (0,6), (3,17), (–2, –1)}:Which equation is true?
f(-10)=1
f(2)=-10
f(0)=6
f(1)=-10
The answer choices are :
f (-10) = 1 values x = -10, f (x) = y = 1, ordered pairs (-10,1)
f (2) = - 10 values x = 2, f (x) = y = -10, ordered pairs (2, -10)
f (0) = 6 value x = 0, f (x) = y = 6, ordered pairs (0.6)
f (1) = - 10 values x = 1, f (x) = y = -10, ordered pairs (1, -10)
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The following three shapes are based only on squares, semicircles, and quarter circles.
Find the perimeter and the area of each shaded part.
The perimeter of the shaded part is: 25.1 cm.
The area of the shaded part is: 36.6 cm².
How to Find the Perimeter and Area of the Shaded Part?Area = Area of square - 2(area of square - area of quarter circle) = s² - 2(s² - 1/4πr²).
Parameters given are:
s = 8 cmr = 8 cmPlug in the values into the equation
Area = 8² - 2(8² - 1/4π(8²)).
Area = 64 - 2(64 - 50.3)
Area = 36.6 cm²
Perimeter = 2(perimeter of quarter circle) = 2(1/4(2πr)) = 2(1/4(2π8)) = 25.1 cm
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A certain positive integer has exactly 20 positive divisors. What is the smallest number of primes that could divide the integer
As per my explanation to (b) above, the largest number of primes that could factor such a number is 4.
Note that 2,3,5 and 7 are the smallest primes, then use the reasoning from
(b) above. we are looking for four exponents, that, when 1 is added to each and all are multiplied together, would equal 20.
But no such integers k, l, m, and n exist such that (k + 1)(l + 1)(m + 1) (n + 1) = 20 where k, l,m, and n ≥ 1 so this number, whatever it is, can't have 4 prime factors
Let's drop 7 out of the mix and suppose it has just 3 prime factors 2, 3, and 5 again we are looking for three exponents, that, when 1 is added to each and all are multiplied together, would equal 20. Put another way, we are looking for k, l and m ≥ 1 such that (k + 1)(l + 1)(m + 1) = 20
Note that the only possibility here is when we have 2 *2 *5 = 20 and the smallest possible product would be 2^(4 )* 3^(1) * 5^(1) = 2^4 * 3 * 5 = 240
Now......the only remaining possibility is that this number is composed of the two smallest primes, 2 and 3, and we are looking for some k and l ≥ 1 such that (k + 1)(l + 1) = 20 clearly, the only possibilities are when k = 4 and l = 5, or vice-versa
So this number would factor as either 2^3 * 3^4 = 648 or 2^4 * 3^3 = 432 and both are > 240.
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What is 12.1975 rounded to the nearest thousandth?
Answer:
12.198
hope it helps
12.198
To round over 7 into 8, the ten-thousandth place needs to be 5 or over, and as we can see the ten-thousandth place is 5.
Use the figure to decide the type of angle pair that describes ∠5 and ∠6.
Reason:
These angles are both in the same corresponding direction. Both are in the same western corner, or point to the west. If the lines were parallel, then the corresponding angles would be congruent.
Terrell brought 42 muffins to school for his birthday He gave one each to the 17students in his class and to the 19 student in the other third grade class
Answer:
The expression is 42-17-19 OR 42-(17+19).
Step-by-step explanation:
First, we can indicate that we can use subtraction because is giving them away for his birthday.
"He gave one each to the 17 students in his class and to the 19 students in the other third-grade class".
That represents taking away 17 and 19 means that it is subtracting them.
Hope this helps. (:
E represents a number. For example, if E is 5, EE equals 55 and 4E equals 45. If 1E x E = 9E, what number should be in the place of E?
Answer:
E represents a number, for this question we need to keep in mind that the product of 1E and E must end in E.
E must be 6.
E = 6
Step-by-step explanation:
16 * 6 = 96
A student submitted the following work that is not correct. Can you find the mistake?
Explain the mistake the student made.
Simplify (assuming all variables are positive): √32x³y²z7
Step 1: √8.4.x².xy².26. z
Step 2: 2xyz³ √8xz
Step-by-step explanation:
so you have the equation: [tex]\sqrt{32x^3y^2z^7}[/tex] which I'm assuming is what you meant to input. and the next step I'm assuming you wrote: [tex]\sqrt{8} * \sqrt{4} * \sqrt{x^2} * \sqrt{y^2} * \sqrt{x} * \sqrt{z^6} * \sqrt{z}[/tex], although I'm not 100% sure, I'm basing this assumption off of step 3. Anyways this will simplify to [tex]2xyz^3\sqrt{8xz}[/tex] which is correct kind of, but since they were asked to FULLY SIMPLIFY, then it's not completely done. This is because 8 has a factor of 4 which is a perfect square. This is because in step 1, the student rewrote 32 as sqrt(8) * sqrt(4) instead of writing it as sqrt(2) * sqrt(16) which is the greatest factor of 32 that is a perfect square. So they could've either done that in step 1, or they could've realized in step 2, that they can further simplify sqrt(8) and then have a step 3 showing that.