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 Depdendent Variable

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 Dependent Variable

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# Rationalizing the Denominator

Example 1

Simplify:

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,