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Rationalisation

by Joseph
(Bangalore, India)











































When a fraction contains a radical, calculation of the decimal value for the fraction can be difficult.

This calculation can be simplified by removing the radical from the denominator.

Removing the radical from the denominator is called "Rationalizing the Denominator".

Rationalize √2 / √3

Comments for Rationalisation

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Jun 07, 2011
Rationalisation
by: Staff

The question:

Rationalise √2 / √3


The answer:

You can rationalise either the numerator or the denominator of your fraction.

Rationalising the Denominator is the standard way of simplifying fractions containing radicals in the denominator. Rationalising the denominator means to “rewrite the fraction so there are no radicals in the denominator”.

Your problem:

= √(2) / √(3)


“IF” the denominator could by multiplied by itself [the sqrt(3)], then the √ sign in the denominator would disappear, since:

√(3) * √(3) = √(3*3) = √(3²) = 3


However, in order to preserve the value of the original fraction, both the numerator and denominator must each be multiplied by the same amount: √(3).

To apply this concept, multiply the original fraction by √(3)/√(3). The fraction √(3)/√(3) 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] * √(3) / √(3)

= [original fraction] * 1

= [original fraction]


Therefore,

= [original fraction] * √(3) / √(3)

= [√(2) / √(3)] * [√(3) / √(3)]

Multiply the numerators of the two fractions together and the denominators of the two fractions together

= [√(2) * √(3)] / [√(3) * √(3)]

Since the two square root expressions in the numerator are multiplied together, they can be combined under one radical sign


= [√(2 * 3)] / [√(3) * √(3)]

= [√(6)] / [√(3) * √(3)]

Since the two square root expressions in the denominator are multiplied together, they can also be combined under one radical sign

= [√(6)] / [√(3 * 3)]

= [√(6)] / [√(3²)]

Take the square root of the denominator

= [√(6)] / 3




The final answer is:

√(2) / √(3) = [√(6)] / 3





Thanks for writing.

Staff
www.solving-math-problems.com



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