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

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Answer 1 · 2015-09-17T18:19:27

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

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 $2(17-12sqrt(2))$ .

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