Algebra of irrational numbers

Question

Why is $$\sqrt{7 + 2\sqrt{10}} = \sqrt2 + \sqrt5 $$

I can't seem to prove it so can someone help me out in doing so if it is possible.

And if it can't be proven, is there and explanation to why this is so?

Answer 1

Hint. Note that $7 + 2\sqrt{10}=2+2\sqrt{2}\sqrt{5}+5$.

Answer 2

Hint: One way to verify a (proposed) square root is to square the answer.

Answer 3

Hint: What happens when you square both sides of the equation? Positive numbers have $2$ (real) square roots, how can you distinguish between the $2$?