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.)