# -3/the square root of 6, Rationalize the Denominator

(Tennessee)

-3/the square root of 6. I know that it multiplies out to -3 square root of 6/6, but do you reduce it to-square root of 6/2 or leave it as -3square root of 6/6? Thanks.

### Comments for -3/the square root of 6, Rationalize the Denominator

 Nov 16, 2010 Rationalizing the Denominator by: Staff The question: Rationalize the denominator for the following fraction: -3/the square root of 6. I know that it multiplies out to -3 square root of 6/6. Do you reduce it to-square root of 6/2 or leave it as -3square root of 6/6? Thanks. The answer: -3/sqrt(6) We are not going to change the value of -3/sqrt(6). We are merely rearranging it so that there will be no sqrt in the denominator. To rationalize the denominator, multiply the fraction -3/sqrt(6) by another fraction: sqrt(6)/sqrt(6). [Note that the second fraction sqrt(6)/sqrt(6) = 1, so you are really multiplying by 1. Multiplying -3/sqrt(6) by 1 does not change its value. Why choose the fraction sqrt(6)/sqrt(6)? Why not some other fraction? I deliberately chose to put the sqrt(6) in both the numerator and denominator because I know that sqrt(6) * sqrt(6) will equal the rational number 6] [-3/sqrt(6)] * [sqrt(6)/sqrt(6)] = [(-3) * sqrt(6)] /[sqrt(6) * sqrt(6)] = -3sqrt(6) /6 Without reducing the fraction any further, the answer is: -3sqrt(6) /6 In general, it’s a good idea to check your final answer with a calculator when you can. Google’s free on-line calculator is located here: http://www.google.com/intl/en/help/features.html#calculator Check the numerical result for your original problem: Just enter -3/sqrt(6), then press carriage return According to Google: (-3) / sqrt(6) = -1.22474487 Check the numerical result for your version with the rationalized denominator: Just enter -3sqrt(6) /6, then press carriage return According to Google: ((-3) sqrt(6)) / 6 = -1.22474487 Notice that the numerical results for both versions of the expression are the same. That means that we rationalized the denominator correctly. -3/sqrt(6) = -3sqrt(6) /6 , exactly The answer to your second question is Yes, you can reduce the answer to a simpler form. Begin by factoring the denominator: -3sqrt(6) /6 = [-3 * sqrt(6)] /[2 * 3] The 3 in the numerator cancels the 3 in the denominator. [-3 * sqrt(6)] /[2 * 3] = -1 * sqrt(6)] /2 -1 * sqrt(6)] /2 = -sqrt(6)/2 The final answer to your problem is: -sqrt(6)/2 Thanks for writing. Staff www.solving-math-problems.com