The value of $\frac{1}{\sqrt{17 + 12\sqrt{2}}}$ is closest to _____.

0.17

The value of $\frac{1}{\sqrt{17 + 12\sqrt{2}}}$ = ?

If we consider $\frac{1}{\sqrt{17 + 12\sqrt{2}}}$ = x and 17 = a and 12\(\sqrt {2}\) = b and the difference between the square of them is 1 then the value of  $\frac{1}{\sqrt{17 + 12\sqrt{2}}}$ = \(\sqrt {17 - 12\sqrt{2} }\)

so, \(\sqrt {17 - 12\sqrt{2} }\) = \(\sqrt {(3 - \sqrt{8})^2 }\)

 = 3 - $\sqrt{8}$

= 3 - 2.83

$\frac{1}{\sqrt{17 + 12\sqrt{2}}}$ = 0.17