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# Simplify radical expressions by rationalizing the denominator

To simplify radical expressions by rationalizing the denominator it will be useful to remember the following properties.

• The multiplication property of square roots states that

• The division property of square roots states that

Simplify

To simplify this radical expression, rewrite it with a radical in the numerator and a radical in the denominator. Then factor out any perfect squares and simplify.

=   Find the prime factorizations of the numerator and denominator
=   Apply the division property of square roots

To finish simplifying the expression, multiply by to rationalize the denominator.

=

Simplify
=

Simplify the denominator
=   Multiply

Simplify.           