# Lesson 2

Square Roots and Cube Roots

### Problem 1

Rewrite the following expression as a number with no exponents. Explain or show your reasoning.
$$\displaystyle \dfrac{7^{\text-3}}{7^{\text-5}}$$

### Solution

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(From Unit 3, Lesson 1.)

### Problem 2

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

1. $$(2^d)^4 = 2^{12}$$
2. $$3^5 \boldcdot 7^5 = e^5$$
3. $$5^0 \boldcdot 5^f = 5^4$$

### Solution

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(From Unit 3, Lesson 1.)

### Problem 3

A square has area 9 cm2. How long are its sides?

A:

3 cm

B:

4.5 cm

C:

9 cm

D:

81 cm

### Solution

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### Problem 4

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

 side length (cm) area (cm2) 5 $$\sqrt{63}$$ $$\sqrt{125}$$ 49 98 102

### Solution

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### Problem 5

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

### Solution

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