Dynamic Activity

Operations With Radical Expressions

Lesson Vocabulary

• like radicals
• unlike radicals
• conjugates

Problem 1 Combining Like Radicals

What is the simplified form of each expression?

1. 6 11 + 9 11 6 square root of 11 plus 9 square root of 11

   Think

   Have you seen a problem like this before?

   Yes. Combining like radicals is similar to combining like terms. For example, simplifying the expression in part (A) is similar to simplifying 6x + 9x.

   6 11 + 9 11 = ( 6 + 9 ) 11 Use the Distributive Property to combine like radicals .   = 15 11 Simplify . table with 2 rows and 3 columns , row1 column 1 , 6 square root of 11 plus 9 square root of 11 , column 2 equals . open , 6 plus 9 , close . square root of 11 , column 3 cap usethecap distributivecap propertytocombinelikeradicals . . , row2 column 1 , , column 2 equals 15 , square root of 11 , column 3 cap simplify , . , end table

2. 3 − 5 3 square root of 3 minus 5 square root of 3

   3 − 5 3 = 1 3 − 5 3 Write   3   as   1 3 .   = ( 1 − 5 ) 3 Use the Distributive Property to combine like radicals .   = − 4 3 Simplify . table with 3 rows and 3 columns , row1 column 1 , square root of 3 minus 5 square root of 3 , column 2 equals 1 square root of 3 minus 5 square root of 3 , column 3 cap write , square root of 3 as 1 square root of 3 . , row2 column 1 , , column 2 equals . open , 1 minus 5 , close . square root of 3 , column 3 cap usethecap distributivecap propertytocombinelikeradicals . . , row3 column 1 , , column 2 equals negative 4 square root of 3 , column 3 cap simplify , . , end table

✓ Got It?

1. What is the simplified form of each expression?
   1. 7 2 − 8 2 7 square root of 2 minus 8 square root of 2
   2. 5 5 + 2 5 5 square root of 5 plus 2 square root of 5