How do you evaluate (2\sqrt { 2} - \sqrt { 7} ) ^ { 2}?

1 Answer
Dec 7, 2016

(2sqrt2 - sqrt7)^2 simplifies to -4sqrt(14) + 15.

Explanation:

For the square of any binomial, it follows this general rule: (x - y)^2 = x^2 - 2xy + y^2. We can apply this here where x is 2sqrt2 and y is sqrt7

(2sqrt(2) - sqrt(7))^2
= (2sqrt2)^2 - 2(2sqrt2)(sqrt7) + (sqrt7)^2
= 8 - 4sqrt(7*2) + 7
= -4sqrt(14) + 15

So, our final simplified answer is -4sqrt(14) + 15.