Page 464 - Algebra 1

L E S S O N Adding and Subtracting Radical Expressions 69
Warm Up
1. Vocabulary Terms that have the same variable(s) raised to the same
(18)
Simplify.
2. 3s + 4t + 8s - 7t
(18)
4. √ 72 (61)
power(s) are called .
3. 9wv - 4m + 13m - 17wv (18)
5. √ 50 (61)
New Concepts Combining radicals is similar to combining like terms. When combining radical expressions, use like radicals. Like radicals have the same radicand and
index. Unlike radicals have different radicands and/or index numbers.
Combining Like Radicals
Simplify. All variables represent non-negative real numbers. a. 2√ 7 + 4√ 7
Math Language
A radicand is the number or expression under a radical symbol.
Example
1
SOLUTION
Add the like radicals together. 2√ 7 + 4√ 7 = (2 + 4)√ 7
= 6 √ 7 b . 4 √ x y - 6 √ x y
SOLUTION
Combine coefficients of like radicals.
Combine coefficients of like radicals.
Subtract the like radicals.
4 xy - 6 xy = (4 - 6) xy
Online Connection www.SaxonMathResources.com
d. 2√ 5q + 3√ 5q - 4√ 3r ___
777
SOLUTION
2√ 5q + 3√ 5q + 4√ 3r ___
777
= (2 + 3)√ 5q - 4√ 3r ___
= 5√ 5q - 4√ 3r _7_ 7
7
Combine the like radicals. Simplify.
√ √ √
=-2 xy √
c. 6√2 +8√ 11 SOLUTION
No simplification is possible since the radicands are not alike.
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