Question

homework:
ch. 9.3 square roots and cube roots
square roots and cube roots
apply your knowledge of square roots and cube roots to answer each question.

1. which of the following is a true statement?

a. squaring a number is the same as
multiplying the number by 2.
b. taking the cube root of a number is the
inverse operation of raising a number to
the 3^rd power.
c. both a and b are true.
d. neither a nor b is true.

1. joel needs to solve the equation below.

which describes the step he should take?
n² = 16
a. divide both sides by 2
b. take the square root of both sides
c. square both sides
d. none of the above

1. evaluate each expression in a - d.

a. (-9)² = ______
b. 2³ = ______
c. √256 = ______
d. ∛125 = ______
in 4 - 7, use inverse operations to find the value of the variable needed to make the equation true.
4.
x² = 169
______
5.
b³ = 343
______
6.
n² = 625
______
7.
a³ = 1,000
______

1. three students solved the equations shown.

use the clues to write the name of the student who
solved each equation above the correct box.

• huey and liam’s equation have the same solution.
• nadia’s equation has a solution that is greater than 10.
• huey’s equation can be solved by taking the cube root of both sides.

a pyramid has a square base with an area of 144 ft². mark each statement as true or false and
correct any false statements.
______ 9. the length of one side of the pyramid’s base can be found using the equation
s² = 144.
______ 10. the length of one side of the pyramid’s base is 72 feet.

Explanation:

Step1: Analyze Q1 statements

• a. Squaring: $n^2

eq 2n$ (e.g., $3^2=9, 2*3=6$) → False.

• b. Cube root is inverse of $n^3$: $\sqrt[3]{n^3}=n$ → True.

Step2: Solve Q2 equation step

For $n^2=16$, inverse of squaring is square root.

Step3: Evaluate Q3 expressions

a. $(-9)^2 = (-9)*(-9) = 81$
b. $2^3 = 2*2*2 = 8$
c. $\sqrt{256} = 16$ (since $16^2=256$)
d. $\sqrt[3]{125} = 5$ (since $5^3=125$)

Step4: Solve Q4-7 via inverse ops

1. $x^2=169$ → $x=\pm\sqrt{169}=\pm13$
2. $b^3=343$ → $b=\sqrt[3]{343}=7$
3. $n^2=625$ → $n=\pm\sqrt{625}=\pm25$
4. $a^3=1000$ → $a=\sqrt[3]{1000}=10$

Step5: Match Q8 equations to students

• Huey: Uses cube root → $y^3=729$ (solution $9$)
• Liam: Same solution as Huey → $x^2=81$ (solution $\pm9$)
• Nadia: Solution >10 → $w^2=121$ (solution $\pm11$)

Step6: Verify Q9-10 base side

1. Square area: $s^2=144$ → True.
2. $s=\sqrt{144}=12

eq72$ → False.

Answer:

1. b. Taking the cube root of a number is the inverse operation of raising a number to the 3rd power.
2. b. Take the square root of both sides
3. a. $81$; b. $8$; c. $16$; d. $5$
4. $x = \pm 13$
5. $b = 7$
6. $n = \pm 25$
7. $a = 10$
8. $w^2=121$: Nadia; $x^2=81$: Liam; $y^3=729$: Huey
9. True
10. False; The length of one side of the pyramid’s base is 12 feet.