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

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Answer 1 · 2018-04-17T04:25:27

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

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!