Find the square root of $7-2\sqrt{10}$.

We have to find the $\sqrt{7-2\sqrt{10}}$.

Now we can write the above expression as
= $\sqrt{7-2\sqrt{2 . 5 }}$

As we know $\sqrt{\mathit{ab}}=\sqrt{a}\sqrt{b}$
Therefore, by applying the above formula, we get:

= $\sqrt{7-2\sqrt{5}\sqrt{2}}$

Now by rewriting the 7 as 5 + 2, we get:

= $\sqrt{5+2-2\sqrt{5}\sqrt{2}}$

Now, as we know that a²−2ab+b²=(a−b)²

So, by applying the formula and substituting the values, we get:

= $\sqrt{{\left(\sqrt{5}-\sqrt{2}\right)}^2}$
Therefore, now on applying the rule  $\sqrt{a^2}=\left|a\right|$, we get:

$\left|\left(\sqrt{5}-\sqrt{2}\right)\right|$

And it can also be written as  $\left(\sqrt{5}-\sqrt{2}\right)$.