Simplifying Square Roots and Cube Roots

A whole number whose square root is an integer is referred to as a perfect square. Consider the following example:

√9 = 3

Because √9 is an integer, 9 is a perfect square. Consider, however, √8.

√8 ≈ 2.828427125

Because √8 is irrational, 8 is not a perfect square. To determine √8, you could use the calculator to find a decimal approximation. You would then notice that the value lies between 2 and 3. Another option is to represent √8 in simplest radical form, or in other words, to represent it as a radical expression where the radicand has no perfect square factors other than 1. In this topic, you will learn how to represent radical expressions in simplest form.

Essential Questions

• How can you simplify square roots of whole numbers?
• How can you simplify square roots of monomial algebraic expressions?
• How can you simplify cube roots of integers?