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

1 Answer
Sep 8, 2015

Answer:

#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#