10.2 Simplifying Radical Expressions A radical expression is in simplest form if and only if: 1. The radicand has no perfect square factors other than one. 2. There are no fractions in the radicand 3. The denominator does not contain a radical expression. Simplify the following: 50 Consider x2 When finding the principal square root of an expression containing variables, be sure that the result is not negative. x2 ? = x (What if x = -3 ? ) ? (-3)2 = -3 9 3 ? = -3 = -3 When the exponent of the variable inside a radical is even and the simplified exponent is odd, must use absolute value. x2 = | x | 2 x5 = x x3 = x x x 6 = x3 x Simplify: 4 5 32 x y z6 x 4 = x2 7 9 48 8 32 50 7 6 35 15 24 x3 Multiply: ( 3 + 5 (( 3 - 5 ( Simplify: 4 - 3 2 2 4 + 5
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