How do do you rationalize the square root of 5 divided by the square root of 8?

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How do do you rationalize the square root of 5 divided by the square root of 8?

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Answer 1 · 2015-09-08T08:28:27

$sqrt5/sqrt8 = color(green)(sqrt10/4$

Explanation:

Rationalisation is simply expressing a fraction in a form that has a rational denominator .

$sqrt5/sqrt8$ is the fraction that we have been given

The denominator $sqrt 8$ is irrational. To convert it to a rational number, we can multiply the numerator and the denominator of the fraction by $sqrt2$

$sqrt5/sqrt8 = (sqrt5*sqrt2)/(sqrt8*sqrt2)$

We know that $color(blue)(sqrta*sqrtb = sqrt(ab)$
Hence $(sqrt5*sqrt2)/(sqrt8*sqrt2) = sqrt(5*2)/sqrt(8*2) = sqrt 10/sqrt16 = sqrt10/4$

Now the denominator 4 is rational. Hence we can be sure that we have rationalised the denominator

$sqrt5/sqrt8 = color(green)(sqrt10/4$

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How do do you rationalize the square root of 5 divided by the square root of 8?

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