Question

Find the square root of $17-12\sqrt{2}$.

Answer 1

Now,

$17-12\sqrt{2}$

$=17-\mathrm{2.3.2}\sqrt{2}$

$=3^2+(2\sqrt{2}{)}^2-\mathrm{2.3.2}\sqrt{2}$

$=(3-2\sqrt{2}{)}^2$.

Now square root of $17-12\sqrt{2}$ is $\pm (3-2\sqrt{2})$.