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	Conjugates
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	Solving One-Step Equations Using Models
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	Adding and Subtracting Polynomials
	Rationalizing the Denominator
	Rounding Off
	The Distributive Property
	What is a Quadratic Equation
	Laws of Exponents and Multiplying Monomials
	The Slope of a Line
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	Multiplying and Dividing Rational Expressions
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Rationalizing the Denominator

Example 1

Simplify:

Solution
Factor the radicand.

The radical in the denominator is a cube root. To rationalize the denominator, we want to make the radicand a perfect cube.

2 occurs twice as a factor. To make a perfect cube, we multiply by 2.
w occurs once as a factor. To make a perfect cube, we multiply by w².

We multiply by 1 written in the form
Multiply the numerators and multiply the denominators.
Simplify the denominator.
So,

Suppose we have a radical expression such as

Recall that when we multiply conjugates, the result is always a rational number.

Therefore, to eliminate the radical in the denominator of the expression, we multiply the numerator and denominator by , the conjugate of the denominator.

Example 2

Simplify:

Solution
To rationalize the denominator we multiply the numerator and denominator by , the conjugate of x
Multiply the numerators and multiply the denominators.
Remove the parentheses.
Simplify the denominator. The two middle terms add to zero.
So,