10-2 Simplifying Radicals

Objective

To simplify radicals involving products and quotients

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In the Solve It, the maximum height of the mirror is a radical expression. A radical expression, such as 2 3 2 square root of 3  or x + 3 , square root of x plus 3 end root , comma  is an expression that contains a radical. A radical expression is simplified if the following statements are true.

• The radicand has no perfect-square factors other than 1.
• The radicand contains no fractions.
• No radicals appear in the denominator of a fraction.

Simplified Not Simplified 3 5 9 x 2 4 3 12 x 2 5 7 table with 2 rows and 2 columns , row1 column 1 , cap simplified , column 2 cap notcap simplified , row2 column 1 , 3 square root of 5 9 square root of x , fraction square root of 2 , over 4 end fraction , column 2 3 square root of 12 , square root of x over 2 end root . fraction 5 , over square root of 7 end fraction , end table

Essential Understanding You can simplify radical expressions using multiplication and division properties of square roots.

You can use the Multiplication Property of Square Roots to simplify radicals by removing perfect-square factors from the radicand.

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