Stumped on a Q

Sqrting the individual terms

The answer that $\sqrt{a^2+b^2}=a+b$ is horrendous.

This suggests that $5=\sqrt{3^2+4^2}=3+4=7$

What?! How do you guys do this!?

Show that $17(1-\dfrac{1}{17^2})^\frac{1}{2}=n\sqrt{2}$, when n is an integer, whose value is to be found.

I can't see how to do this without sqrting an "unfinished" bracket:

$17(1-\frac{1}{17^2})^\frac{1}{2} = 17(17^0 - 17^{-2})^\frac{1}{2}$

Sqrting the individual terms (I know is wrong) but would give $17(1-17^{-1}) = 16$.

Any clues would be greatly appreciated

*The answer booklet says n = 12

Show that $17(1-\dfrac{1}{17^2})^\frac{1}{2}=n\sqrt{2}$, when n is an integer, whose value is to be found.

I can't see how to do this without sqrting an "unfinished" bracket:

$17(1-\frac{1}{17^2})^\frac{1}{2} = 17(17^0 - 17^{-2})^\frac{1}{2}$

Sqrting the individual terms (I know is wrong) but would give $17(1-17^{-1}) = 16$.

Any clues would be greatly appreciated

*The answer booklet says n = 12

What?! How do you guys do this!?