Radicals allow us to reverse exponent operations. For example, squaring a number such as 5, or (-5) will give us 25. If we take the square root of 25, we get back to 5 or (-5). The same process occurs when we look at higher level roots. A cube root will undo cubing a number. A fourth root will undo raising a number to the fourth power.

Test Objectives
• Demonstrate the ability to evaluate a radical expression
• Demonstrate an understanding of the terms "perfect square" and "perfect cube"
• Demonstrate the ability to simplify a radical expression

#1:

Instructions: Evaluate each.

$$a)\hspace{.2em}\sqrt{121}$$

$$b)\hspace{.2em}\sqrt[3]{-64}$$

#2:

Instructions: Evaluate each.

$$a)\hspace{.2em}-\sqrt[4]{625}$$

$$b)\hspace{.2em}\sqrt[5]{-243}$$

#3:

Instructions: Determine if true or false.

a) 343 is a perfect square

b) 216 is a perfect cube

#4:

Instructions: Simplify each.

Assume all variables represent real numbers (positive, negative, or zero)

$$a)\hspace{.2em}\sqrt{x^{10}y^4}$$

$$b)\hspace{.2em}\sqrt[3]{x^{15}y^{21}}$$

#5:

Instructions: Simplify each.

Assume all variables represent real numbers (positive, negative, or zero)

$$a)\hspace{.2em}\sqrt{x^2 - 18x + 81}$$

$$b)\hspace{.2em}\sqrt[3]{x^3 - 9x^2 + 27x - 27}$$

Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}11$$

$$b)\hspace{.2em}-4$$

#2:

Solutions:

$$a)\hspace{.2em}-5$$

$$b)\hspace{.2em}-3$$

#3:

Solutions:

a) false

b) true

#4:

Solutions:

$$a)\hspace{.2em}|x^5| \cdot y^2$$

$$b)\hspace{.2em}x^5y^7$$

#5:

Solutions:

$$a)\hspace{.2em}|x - 9|$$

$$b)\hspace{.2em}x - 3$$