Question

Rationalize the denominators. $$\frac{8}{\sqrt{6}-2}$$

   Rationalize the denominators.
$$\frac{8}{\sqrt{6}-2}$$

Beginning and Intermediate Algebra

Beginning and Intermediate Algebra

Julie Miller,Molly… 3rd Edition

Chapter 10, Problem 65

Instant Answer

Solved by Expert Prashansha Kaushik

03/29/2021

Step 1

So, we get: $$\frac{8}{\sqrt{6}-2} \times \frac{\sqrt{6}+2}{\sqrt{6}+2}$$ Show more…

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Rationalize the denominators. $$\frac{8}{\sqrt{6}-2}$$

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Key Concepts

Conjugate Method

The conjugate method involves multiplying the numerator and denominator by the conjugate of the denominator. When the denominator is a binomial containing a radical, the product of the binomial and its conjugate results in a difference of squares, which eliminates the radical and leads to a rational denominator.

Rationalizing the Denominator

Rationalizing the denominator is the process of eliminating radicals or irrational numbers from the denominator of a fraction. This is usually done by multiplying the numerator and denominator by an appropriate expression that will remove the radical from the denominator, making the expression simpler to work with.

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