How do you rationalize the denominator sqrt(x/5)?

1 Answer
Apr 17, 2018

The rationalized fraction is sqrt(5x)/5.

Explanation:

Split the radical:

color(white)=sqrt(x/5)

=sqrtx/sqrt5

Then multiply the top and bottom by sqrt5:

=sqrtx/sqrt5color(red)(*sqrt5/sqrt5)

=(sqrtx*sqrt5)/(sqrt5*sqrt5)

=(sqrtx*sqrt5)/((sqrt5)^2)

=(sqrtx*sqrt5)/5

=(sqrt(x*5))/5

=sqrt(5x)/5

That's it. Hope this helped!