Given area of square $= 9+6\sqrt{2}$ Without calculator show its length in form of $(\sqrt{ c}+\sqrt{ d})$ $\sqrt{9+6\sqrt{2}}$  to find length 
But how do I express the above in the form of $\sqrt{c} + \sqrt{d}$. 

Notice, let the side of the square be $a$ then its area is given as $$a^2=9+6\sqrt 2$$
$$a^2=9+2(3)\sqrt 2$$ $$a^2=9+2(\sqrt 3\sqrt 3)\sqrt 2$$
$$a^2=9+2(3)\sqrt 2$$ $$a^2=9+2(\sqrt 3\sqrt 2)(\sqrt 3)$$
$$a^2=6+3+2\sqrt{6}\sqrt 3$$ $$a^2=(\sqrt 6)^2+(\sqrt 3)^2+2(\sqrt{6})(\sqrt 3)$$
Using $a^2+b^2+2ab=(a+b)^2$, we get $$a^2=(\sqrt 6+\sqrt 3)^2$$
hence, side of square $$a=\color{red}{\sqrt6+\sqrt 3}$$
