22. Find the value of $\sqrt{45-\sqrt{2000}}+\sqrt{45+\sqrt{2000}}$.
22. Answer: 10
Let $x_{1}=\sqrt{45-\sqrt{2000}}$ and $x_{2}=\sqrt{45+\sqrt{2000}}$. Then $x_{1}^{2}+x_{2}^{2}=90$ and
$$
x_{1} x_{2}=\sqrt{(45-\sqrt{2000})(45+\sqrt{2000})}=\sqrt{45^{2}-2000}=\sqrt{25}=5
$$

Thus
$$
\left(x_{1}+x_{2}\right)^{2}=x_{1}^{2}+x_{2}^{2}+2 x_{1} x_{2}=100 .
$$

As both $x_{1}$ and $x_{2}$ are positive, we have $x_{1}+x_{2}=10$.