Question

Expand:

`(sqrt(5) + sqrt(2))^2`

Answer 1

To expand `(sqrt(5) + sqrt(2))^2`,

Use the identity:

(a + b)² = a² + 2ab + b²

Let `a = sqrt(5), b = sqrt(2)`

Then: `(sqrt(5) + sqrt(2))^2`

= `(sqrt(5))^2 + 2(sqrt(5))(sqrt(2)) + (sqrt(2))^2`

= `5 + 2sqrt(10) + 2`

= `7 + 2sqrt(10)`