Question

1. relate the volume of the cube to the length of each edge.
2. relate the area of the square to the length of each side.
3. a square technology chip has an area of 25 square centimeters. how long is each side of the chip?
4. the volume of cube a is 125 cubic inches. the face of cube b has an area of 36 square inches. which cube has a greater side length?

11 and 12, plot, compare, and order the square roots, cube roots, and expressions.

1. $sqrt{10^{2}-8^{2}},sqrt3{ - 8},(\frac{1}{2})^{2}+sqrt{9}$
2. $sqrt{121},4^{2}-sqrt3{(3^{3}-19)},(-1)^{3}+sqrt{81}$
3. amy is making building blocks. what is the length of each side of the block?

1 - 3 evaluate square roots and cube roots

Explanation:

7.

Step1: Recall volume formula for cube

The volume formula for a cube is $V = s^3$, where $s$ is the edge - length. Given $V = 8\ cm^3$, we need to find $s$ such that $s\times s\times s=8$.

Step2: Calculate the cube - root

We know that $\sqrt[3]{8}$, and since $2\times2\times2 = 8$, $\sqrt[3]{8}=2$.

Step1: Recall area formula for square

The area formula for a square is $A = s^2$, where $s$ is the side - length. Given $A = 16\ cm^2$, we need to find $s$ such that $s\times s = 16$.

Step2: Calculate the square - root

We know that $\sqrt{16}$, and since $4\times4 = 16$, $\sqrt{16}=4$.

Step1: Use area formula for square

For a square with area $A = 25\ cm^2$, using the formula $A=s^2$, we solve for $s$ by taking the square - root of both sides.

Step2: Calculate the side - length

$\sqrt{25}=5$, so each side of the square technology chip is $5$ centimeters long.

Answer:

$2\ cm\times2\ cm\times2\ cm$, $\sqrt[3]{8}=2$

8.