Question

Evaluate:-

$\large\rm{ \Bigg ( \sqrt{ \sqrt { \sqrt { \sqrt{2}}}} \Bigg ) ^{48}}$​

Answer 1

$\large\rm{ \bigg ( \sqrt{ \sqrt { \sqrt { \sqrt{2}}}} \bigg ) ^{48}}$

$\large\rm{ = \Bigg ( \bigg( \Big( \big ( 2^{ \frac{1}{2}} \big)^{ \frac{1}{2}} \Big )^{ \frac{1}{2}} \bigg ) ^{ \frac{1}{2}} \Bigg ) ^{48}}$

$\large\rm{ = 2^{\frac{48}{16}}}$

$\large\rm{ = 2^{3}}$

$\large\rm{ = 8}$