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) 5   \(\sqrt{63}\)     \(\sqrt{125}\)
area (cm2)   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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