Squares, Square Roots, Cubes, and Cube Roots

Squares, Square Roots, Cubes, and Cube Roots

Lesson Objectives

At the end of the lesson, you should be able to:

1. identify the connection between squares and corresponding square roots, and cubes and corresponding cube roots; and

2. solve mathematical problems involving squares, square roots, cubes, and cube roots.

Multiple Choice

Is  8³  the same thing as   $$8\times3$$  ?

• YES

• NO

Multiple Choice

Is   $$\left(-3\right)^2$$   the same thing as  -3² ?

• YES

• NO

Multiple Select

Select all the expressions that are equivalent to 7².

• 14

• 7 x 7

• 7 x 2

• 49

• 7 + 2

Fill in the Blanks

$\sqrt[]{64}+\sqrt[]{36}$

Fill in the Blanks

$\sqrt[]{144}-\sqrt[]{81}$

Fill in the Blanks

$\left(\sqrt[]{25}\right)^{2\ }-\left(\sqrt[]{16}\right)^2$

Fill in the Blanks

$\left(\sqrt[]{4}\right)^{2\ }+\left(\sqrt[]{9}\right)^2$

Fill in the Blanks

$\sqrt[]{9^2}+\sqrt[]{7^2}$

Fill in the Blanks

$-\sqrt[]{3^2}-\sqrt[]{5^2}$

Fill in the Blanks

$-\sqrt[]{5^2}+\sqrt[]{5^2}$

Fill in the Blanks

$6^3$

Fill in the Blanks

$8^3$

Multiple Choice

$$\sqrt[3]{64}=\sqrt[3]{4^3}=4$$

• TRUE

• FALSE

Multiple Choice

$$\sqrt[3]{5^3}=5^3$$

• TRUE

• FALSE

Fill in the Blanks

$\sqrt[3]{27}$

Multiple Choice

$$\sqrt[3]{-64}=-4$$

• TRUE

• FALSE

Fill in the Blanks

$\sqrt[3]{-343}$

Fill in the Blanks

$2\sqrt[3]{8}$

Fill in the Blanks

$\sqrt[3]{-343}+8$

Multiple Choice

$$\sqrt[3]{0}+\sqrt[3]{1}+\sqrt[3]{-125}+\sqrt[3]{512}$$

• 14

• 4

• -4

• -14

Multiple Choice

Find the total surface area of a cube that has a volume of $$125\ cm^3$$ .

• $$30\ cm^2$$

• $$100\ cm^2$$

• $$25\ cm^2$$

• $$150\ cm^2$$

Multiple Choice

Find the total surface area of a cube that has a volume of $$64\ cm^3$$ .

• $$48\ cm^2$$

• $$16\ cm^2$$

• $$24\ cm^2$$

• $$96\ cm^2$$