Question

$73-12\sqrt{35}$

Answer 1

$$\begin{gathered} \sqrt{73-12\sqrt{35}} \\ =\sqrt{73-12\sqrt{7\times 5}} \\ =\sqrt{\left(45+28\right)-12\times \sqrt{5}\times \sqrt{7}} \\ =\sqrt{{\left(3\sqrt{5}\right)}^2+{\left(2\sqrt{7}\right)}^2-2\times 3\sqrt{5}\times 2\sqrt{7}} \\ =\sqrt{{\left(3\sqrt{5}-2\sqrt{7}\right)}^2} \\ =3\sqrt{5}-2\sqrt{7} \end{gathered}$$