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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

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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)/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]


= [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.


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