How to simplify a square root How can the following:
$$
\sqrt{27-10\sqrt{2}}
$$
Be simplified to:
$$
5 - \sqrt{2}
$$
Thanks

$$\sqrt{27 - 10\sqrt{2}}$$
$$= \sqrt{25 + 2 - 2.5.\sqrt{2}}$$
$$= \sqrt{5^{2} - 2.5.\sqrt{2} +{\sqrt{2}}^2}$$
$$= \sqrt{{(5 - \sqrt{2})}^2}$$
$$= (5 - \sqrt{2})$$
$$= R.H.S$$
