# Existence and Uniqueness of Square and Cube Roots

Videos to help Grade 8 students learn that the positive square root and cube root exists for all positive numbers and is unique and solve simple equations that require them to find the square or cube root of a number.

New York State Common Core Math Grade 8, Module 7, Lesson 3

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Lesson Plans and Worksheets for Grade 8

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Lesson 3 Student Outcomes

• Students know that the positive square root and cube root exists for all positive numbers and is unique.
• Students solve simple equations that require them to find the square or cube root of a number.

Lesson 3 Summary

The square or cube root of a positive number exists, and there can be only one positive square root or one cube root of the number.

Lesson 3 Classwork

Opening
Find the Rule Part 1
Find the Rule Part 2
Exercises 1–9
Find the positive value of that makes each equation true. Check your solution.
1. x2 = 169
a. Explain the first step in solving this equation.

2. A square-shaped park has an area of 324 ft2. What are the dimensions of the park? Write and solve an equation.
3. 625 = x2
4. A cube has a volume of 27 in3. What is the measure of one of its sides? Write and solve an equation.
5. What positive value of makes the following equation true: x2 = 64? Explain.
6. What positive value of makes the following equation true: x3 = 64? Explain.
7. x2 = 256-1 Find the positive value of x that makes the equation true.
8. x3 = 343-1 Find the positive value of x that makes the equation true.
9. Is 6 a solution to the equation x2 - 4 = 5x? Explain why or why not.

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