# sqrt(144/x) – Rationalize the Denominator

by Hana
(Rochester, MN,USA)

i need help finding 144 over x and that's all under the square root sign

### Comments for sqrt(144/x) – Rationalize the Denominator

 Jun 06, 2011 Rationalize the Denominator by: Staff The question: by Hana (Rochester, MN, USA) i need help finding 144 over x and that's all under the square root sign The answer: sqrt(144/x) = sqrt(144)/sqrt(x) = sqrt(12²)/sqrt(x) = 12/sqrt(x) Rationalizing the Denominator is the standard way of simplifying fractions containing radicals in the denominator. Rationalizing the denominator means to “rewrite the fraction so there are no radicals in the denominator”. Your problem as it now stands: = 12/√(x) “IF” the denominator could by multiplied by itself [the sqrt(x)], then the √ sign in the denominator would disappear, since: √(x) * √(x) = √(x*x) = √(x²) = x However, in order to preserve the value of the original fraction, both the numerator and denominator must each be multiplied by the same amount: √(x). To apply this concept, multiply the original fraction by √(x)/√(x). The fraction √(x)/√(x) is equal to 1, so the original fraction is merely being multiplied by 1. As you can see by the following illustration, its value has not been changed. = [original fraction] = [original fraction] * √(x)/√(x) = [original fraction] * 1 = [original fraction] Therefore, = [original fraction] * √(x)/√(x) = [(12)/√(x)] * [√(x)/√(x)] = 12 * [√(x)] / [√(x) * √(x)] = [12 * √(x)] / [√(x*x)] = [12 * √(x)] / √(x²) = [12 * √(x)] / x = [12√(x)] / x The final answer is: √(144/x) = [12√(x)]/ x Thanks for writing. Staff www.solving-math-problems.com