# Lesson 13

Cube Roots

### Problem 1

Find the positive solution to each equation. If the solution is irrational, write the solution using square root or cube root notation.

1. $$t^3=216$$

2. $$a^2=15$$

3. $$m^3=8$$

4. $$c^3=343$$

5. $$f^3=181$$

### Problem 2

For each cube root, find the two whole numbers that it lies between.

1. $$\sqrt[3]{11}$$
2. $$\sqrt[3]{80}$$
3. $$\sqrt[3]{120}$$
4. $$\sqrt[3]{250}$$

### Problem 3

Order the following values from least to greatest:

$$\displaystyle \sqrt[3]{530},\;\sqrt{48},\;\pi,\;\sqrt{121},\;\sqrt[3]{27},\;\frac{19}{2}$$

### Problem 4

Select all the equations that have a solution of $$\frac{2}{7}$$:

A:

$$x^2=\frac27$$

B:

$$x^2=\frac{4}{14}$$

C:

$$x^2=\frac{4}{49}$$

D:

$$x^3=\frac{6}{21}$$

E:

$$x^3=\frac{8}{343}$$

F:

$$x^3=\frac67$$

### Problem 5

The equation $$x^2=25$$ has two solutions. This is because both $$5 \boldcdot 5 = 25$$, and also $$\text-5 \boldcdot \text-5 = 25$$. So, 5 is a solution, and also -5 is a solution. But! The equation $$x^3=125$$ only has one solution, which is 5. This is because $$5 \boldcdot 5 \boldcdot 5 = 125$$, and there are no other numbers you can cube to make 125. (Think about why -5 is not a solution!)

Find all the solutions to each equation.

1. $$x^3=8$$
2. $$\sqrt[3]x=3$$
3. $$x^2=49$$
4. $$x^3=\frac{64}{125}$$

### Problem 6

Find the value of each variable, to the nearest tenth.

1.
2.
3.