Page 707 - Algebra 1

Example
2
Rationalizing a Variable Denominator
Simplify √ _5 . All variables represent non-negative numbers. x
SOLUTION
Use the quotient property. Then rationalize the denominator.
√ 5 = √ 5 __
x
Quotient Property of Radicals
Multiply the expression by a factor of 1 that will make the radicand in the denominator a perfect square.
Multiplication Property of Radicals Multiply.
Simplify the square root.
√ x
__ _√x √x
= √ 5 · √ x
= √5 · x
√x · x
= √5 x _
√x = _√ 5 x
x
2
A radical expression is completely simplified when the radicand contains no perfect square factors other than 1, and there are no fractions in the radicand.
Simplifying Before Rationalizing the Denominator
SOLUTION
Example
3
√7 2 x4 _
Simplify 3√2 0 x3 . All variables represent non-negative numbers.
Simplify the numerator and denominator.
___
√7 2 x √ 4 36 · 2 · x2 · x2
3 √ 2 0 x
=
Factor out perfect squares, if possible.
Simplify the radical expressions. Simplify the denominator.
Divide out common factors in the numerator and denominator.
Rationalize the denominator.
Simplify.
Divide out common factors in the numerator and denominator.
Online Connection www.SaxonMathResources.com
6 x 2 √ 2 6 x √ 5 x
_x √ 2 √5 x
x √ 2 · √ 5 x __
_√5 x √5 x x √ 1 0 x
_5x √1 0 x
5
32
= = =
=
= =
__ _2 · 3 · x √ 5 x
3 √ 4 · 5 · x · x 6 x 2 √ 2
692 Saxon Algebra 1