What is the rationaliation factor of root 3
please give answer with explanation

Asked by kckc_kk | 11th Sep, 2016, 01:45: PM

Expert Answer:

begin mathsize 16px style Sometimes space we space come space across space expressions space containing space square space roots space in space their space denominators.
In space such space an space expressions comma space if space the space denominator space is space free space from space square space roots space then space it space will space be space easier space to space add divided by subtract divided by multiply space or space divide. space
To space make space the space denominators space free space from space square space roots comma space we space multiply space the space numerator space and space denominator space by space an space irrational space number. space
Such space straight a space number space is space called space bold rationalization bold space bold factor. space
Note colon
Now space the space rationalizing space factor space of space fraction numerator 1 over denominator square root of straight a end fraction space is space square root of straight a.
So comma space in space our space example comma space the space rationalizing space factor space of space fraction numerator 1 over denominator square root of 3 end fraction space is space square root of 3.
This space is space because comma space in space fraction numerator 1 over denominator square root of 3 end fraction comma space if space we space multiply space the space numerator space and space the space denominator space of space fraction numerator 1 over denominator square root of 3 end fraction space by space square root of 3 comma
that space is space fraction numerator 1 over denominator square root of 3 end fraction cross times fraction numerator square root of 3 over denominator square root of 3 end fraction equals fraction numerator square root of 3 over denominator 3 end fraction.
So comma space our space denominator space is space now space rationalized comma space that space is space we space have space remoed space the space square space root space from space the space denominator.
Since space to space remove space the space square space root space we space multiply space the space numerator space and space the space denominator space of space the space expresssion space by space square root of 3 comma
our space rationalizing space factor space of space fraction numerator 1 over denominator square root of 3 end fraction space is space square root of 3. end style

Answered by Rebecca Fernandes | 11th Sep, 2016, 05:58: PM

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