Simplifying Radical Expressions

A radical expression is in simplest form if no perfect squares other than 1 are in the radicand, no fractions are in the radicand, and no radicals appear in the denominator of the fraction.

Example 1A

Example 1B

Example 1C

Example 1D

Example 1E

Example 1F

Example 1G

Example 1H

The binomials a + and a - are called radical conjugates.

The process of eliminating a radical from an expression’s denominator is called rationalizing the denominator.

Example 2A

Example 2B

Example 2C

Example 2D

The Product Property of Radicals states that the square root of a product equals the product of the square roots of the factors.

Example 3A

Example 3B

Example 3C

Example 3D

The Quotient Property of Radicals states that the square root of a quotient equals the quotient of the square roots of the numerator and denominator.

Example 4A

Example 4B

Example 4C

Example 4D