Question

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

Answer 1

`(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`.