Question:
The value of $\sqrt{248+\sqrt{52+\sqrt{144}}}$ is
(a) 14
(b) 12
(c) 16
(d) 13
Solution:
(c) We have, $\sqrt{248+\sqrt{52+\sqrt{144}}}$
$=\sqrt{248+\sqrt{52+12}}$ $[\because$ square root of $144=12]$
$=\sqrt{248+\sqrt{64}}$
$=\sqrt{248+8}$ $[\because$ square root of $64=8]$
$=\sqrt{256}=16$ $[\because$ square root of $256=16]$