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Answer 1 · 2017-11-07T16:26:18

#6sqrt(2)-6sqrt(3)+sqrt(5)#

#6sqrt(2)-20sqrt(1)/sqrt(5)-sqrt(108)+sqrt(125)#

First you mus get rid of the sqrt in the numerator:

#6sqrt(2)-4*5*(1/sqrt(5))-sqrt(108)+sqrt(125)#

#6sqrt(2)-4sqrt(5)-sqrt(108)+sqrt(125)#

Then decompose the larger number in prime factors:

#6sqrt(2)-4sqrt(5)-sqrt(2^2*3^3)+sqrt(5^3)#

Knownig that #sqrt(a^2)=a# we can do this:

#6sqrt(2)-4sqrt(5)-2*3sqrt(3)+5sqrt(5)#

Simplifing gives:

#6sqrt(2)-6sqrt(3)+sqrt(5)#