6-3 Binomial Radical Expressions

Objective

To add and subtract radical expressions

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Like radicals are radical expressions that have the same index and radicand.

Essential Understanding You can combine like radicals using properties of real numbers.

Here is how you can combine like radicals using the Distributive Property.

Combining radical expressions is different from adding them. The sum of any two real numbers is a real number, so you can add 2 square root of 2  and 3 square root of 3  to get the real number 2 + 3 . square root of 2 plus square root of 3 .

However, you cannot combine the result into a single radical, so 2 + 3 ≠ 5 . square root of 2 plus square root of 3 not equal to square root of 5 .

2 ≈ 1.414 5 ≈ 2.236 + 3 ≈ 1.732   2 + 3 ≈ 3.146 ¯ ≠ 2.236 table with 3 rows and 2 columns , row1 column 1 , square root of 2 almost equal to , 1.414 , column 2 square root of 5 almost equal to , 2.236 , row2 column 1 , plus square root of 3 almost equal to , 1.732 , column 2 , row3 column 1 , square root of 2 plus square root of 3 almost equal to , 3.146 bar , column 2 not equal to , 2.236 , end table

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