Just remove the top 2

Algebra Level 2

$\large \sqrt{2^2} = 2, \qquad \sqrt{2^{2^2}} = 2^2$

The above two equalities are both true.

Continuing with the same pattern, can we also claim that $\large \sqrt{2^{2^{2^2}}} = {2^{2^2}}?$

No Yes

1 solution

Parth Sankhe
Nov 19, 2018

$\sqrt {2^2}=2^{\frac {2}{2}}=2$

$\sqrt {2^{2^2}}=2^{\frac {2^2}{2}}=2^2$

$\sqrt {2^{2^{2^2}}}=2^{\frac {2^4}{2}}=2^8≠2^{2^2}$