Question

Pls help! in solving this queation.

Answer 1

Answer: √2 + 1

Explanation:

$\sqrt{\sqrt{17+12\sqrt2}}$

$=\sqrt{\sqrt{8+12\sqrt2+9}}$

$=\sqrt{\sqrt{(2\sqrt2)^2+2\times(2\sqrt2)\times3+3^2}}$

$=\sqrt{\sqrt{(2\sqrt2+3)^2}}=\sqrt{2\sqrt2+3}$

$=\sqrt{1^2+2\times1\times\sqrt2+(\sqrt2)^2}$

$=\sqrt{(\sqrt2+1)^2}=\sqrt2+1$

Hope it helped