Question

Question #0e278

Answer 1

`3sqrt(2)-4sqrt(5)`

Explanation:

In this question, it was establish that `4sqrt(5)-3sqrt(2)` is a square root of `98-sqrt(10)`. To get the other square root, we can simply multiply by `-1`.

Notice that for any `x`, we have

`x^2 = 1x^2 = (-1)^2x^2 = (-x)^2`

meaning that if `x` is a square root of `x^2`, then so is `-x`. Applying that here, we get the other square root as

`-(4sqrt(5)-3sqrt(2)) = 3sqrt(2)-4sqrt(5)`