# Lesson 2

Square Roots and Cube Roots

- Let’s think about square and cube roots.

### Problem 1

Rewrite the following expression as a number with no exponents. Explain or show your reasoning.

\(\displaystyle \dfrac{7^{\text-3}}{7^{\text-5}}\)

### Problem 2

Find the value of each variable that makes the equation true.

- \((2^d)^4 = 2^{12}\)
- \(3^5 \boldcdot 7^5 = e^5\)
- \(5^0 \boldcdot 5^f = 5^4\)

### Problem 3

A square has area 9 cm^{2}. How long are its sides?

A:

3 cm

B:

4.5 cm

C:

9 cm

D:

81 cm

### Problem 4

The table shows the side length and area of several different squares. Complete the table using exact values.

side length (cm) |
5 | \(\sqrt{63}\) | \(\sqrt{125}\) | |||
---|---|---|---|---|---|---|

area (cm^{2}) |
49 | 98 | 102 |

### Problem 5

Find the two whole numbers that are the closest to \(\sqrt{42}\). Explain your reasoning.