Question

Evaluate : sqrt(1 + sqrt( 1 + sqrt(64))) = ?​

Answer 1

$\Huge\green{\fbox{\red{2}}}$
We have,
$\huge\green{\blue{ \mapsto } \sqrt{1 + \sqrt{1 + \sqrt{64} } } }$
$\huge\green{ = \sqrt{1 + \sqrt{1 + \sqrt{ {8}^{2} } } } }$
$\huge\green{ = \sqrt{1 + \sqrt{1 + 8} } }$
$\huge\green{ = \sqrt{1 + \sqrt{9} } }$
$\huge\green{ = \sqrt{1 + \sqrt{ {3}^{2} } } }$
$\huge\green{ = \sqrt{1 + 3} }$
$\huge\green{ = \sqrt{4} }$
$\huge\green{ = \sqrt{ {2}^{2} } }$
$\huge\green{ = 2}$

$\Huge\green{\fbox{\red{\ddot\smile}}}$$\Huge\green{\fbox{\blue{\ddot\smile}}}$$\Huge\green{\fbox{\orange{\ddot\smile}}}$$\Huge\green{\fbox{\pink{\ddot\smile}}}$