Example 1 Simplify Square Roots

Example 2 Multiply Square Roots

Example 3 Simplify a Square Root with Variables

Example 4 Rationalizing the Denominator

Example 5 Use Conjugates to Rationalize a Denominator

Simplify .

Prime factorization of 52

Product Property of Square Roots

Answer: Simplify.

Simplify .

Product Property of Square Roots

Simplify.

Prime factorization of 72

Answer: Simplify.

Simplify. a.

b.

Answer:

Answer:

Find

Product Property

Answer: Simplify.

Product Property

Find

Answer:

Simplify

Prime factorization

Product Property

Simplify.

The absolute value of ensures a

nonnegative result.

Answer:

Simplify

Answer:

Simplify .

Answer: Simplify.

Product Property of Square Roots

Multiply by .

Simplify .

Prime factorization

Multiply by

Answer: Product Property of Square Roots

Product Property of Square Roots

Prime factorization

Simplify .

Multiply by

Answer: Divide the numerator and denominator

by 2.

Simplify.a.

b.

c.

Answer:

Answer:

Answer:

Simplify

Simplify.Answer:

Simplify

Answer: