Question

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

Answer 1

`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`