How do you simplify #(7sqrt3)/(3-sqrt2)#?

1 Answer
Gió
Jul 28, 2016

I found: #3sqrt(3)+sqrt(6)#

Explanation:

We can try Rationalizing by multiplying and dividing by: #3+sqrt(2)# to get:
#(7sqrt(3))/(3-sqrt(2))*(3+sqrt(2))/(3+sqrt(2))=#
#=(21sqrt(3)+7sqrt(3)sqrt(2))/(9+cancel(3sqrt(2))cancel(-3sqrt(2))-2)=#
#=(21sqrt(3)+7sqrt(6))/7=#
#=21/7sqrt(3)+7/7sqrt(6)=3sqrt(3)+sqrt(6)#

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