How do you simplify #(4-3sqrt2)^2#?

1 Answer
KillerBunny
Sep 17, 2015

The answer is #2(17-12sqrt(2))#

Explanation:

Use the formula #(a-b)^2=a^2+b^2-2ab#, to get

#(4-3sqrt(2))^2= 4^2 + (3sqrt(2))^2 - 2*4*3sqrt(2)#.

#4^2# is, of course, #16#.

#(3sqrt(2))^2# equals #3^2 * (sqrt(2))^2#, which is #9*2=18#.

As for the last term, you simply multiply the factors outside the square root: #2*4*3sqrt(2)=24sqrt(2)#.

Summing everything up, you have #16+18-24sqrt(2)=34-24sqrt(2)#, which you can further simplify into #2(17-12sqrt(2))#.

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