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Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
ISBN: 9781285195728

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Section
BuyFindarrow_forward

Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
ISBN: 9781285195728
Textbook Problem

For Problems 53-76, rationalize the denominator and simplify. All variables represent positive real numbers. (Objective 3)

2 10 - 3

To determine

To rationalize:

The denominator of the given expression 210-3 and simplify the answer as possible.

Explanation

Given radical is,

210-3.

In order to rationalize the binomial denominator:

An expression which contains a binomial denominator with radical, is multiplied by the conjugate of the binomial denominator.

Here, the factors a+b and a-b are called conjugate.

The denominator of the given expression = 10-3

Conjugate of the given denominator = 10+3

Hence, the numerator and denominator of the given expression is multiplied by 10+3 as below,

210-3=210-3·10+310+3

Simplify the above expression,

210-3=210+310-310+3

210-3=210+2310-310+3

Simplify 10-310+3 as below,

10-310+3=1010+3-3(10+3)

10+310-3=1010+103-310-3

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