How do you rationalize the denominator of #sqrt(7/8)#?

1 Answer
Apr 16, 2018

Answer:

#(√14)/ 4#

Explanation:

Rewite as #(√7)/(√8)# to make it easier
The goal here is to find a number that will get rid of the square root in bottom and the best way to do that is just to multiply the bottom by itself.
#((√7)/(√8))*(√8)/(√8)#
#(√56)/(√64)#
#(√56)/8#
Simplify root:
#(√7*2*2*2)/8#
It's a square so take out any numbers that have pairs like two of the #2's# and multiply the rest inside to make #14#
#(2√14)/8#

reduce
#(√14)/ 4#