# Lesson 6

Squares and Square Roots

### Problem 1

Select all solutions to the equation $$x^2=7$$.

A:

$$\sqrt{7}$$

B:

$$\text- \sqrt7$$

C:

49

D:

-49

### Solution

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### Problem 2

Find the solution(s) to each equation, if there are any.

1. $$x^2=9$$
2. $$\sqrt{x}=3$$
3. $$\sqrt{x}=\text-3$$

### Solution

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### Problem 3

1. If $$c$$ is a positive number, how many solutions does $$x^2=c$$ have? Explain.
2. If $$c$$ is a positive number, how many solutions does $$\sqrt{x}=c$$ have? Explain.

### Solution

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### Problem 4

Suppose that a friend missed class and never learned what $$37^{\frac13}$$ means.

1. Use exponent rules your friend would already know to calculate $$(37^{\frac13})^3$$.
2. Explain why this means that $$37^{\frac13}$$ is the cube root of 37.

### Solution

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(From Unit 3, Lesson 3.)

### Problem 5

Evaluate $$8^{\frac53}$$.

### Solution

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(From Unit 3, Lesson 4.)

### Problem 6

Write each expression without using exponents.

1. $$5^{\frac23}$$
2. $$4^{\text-\frac32}$$

### Solution

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(From Unit 3, Lesson 5.)