Question

The value of $y$ such that $\sqrt{188+\sqrt{53+\sqrt{y}}}=14$ is:___

Answer 1

Answer: 6

Given: $\sqrt{188+\sqrt{53+\sqrt{y}}}=14$
Squaring on both side
$188+\sqrt{53+\sqrt{y}}=(14{)}^2$
$\therefore 188+\sqrt{53+\sqrt{y}}=196$
$\therefore \sqrt{53+\sqrt{y}}=196-188$
$\therefore \sqrt{53+\sqrt{y}}=8$
Again squaring on both sides
$53+\sqrt{y}=64$
$\therefore \sqrt{y}=64-53$
$\therefore \sqrt{y}=11$
$\therefore y=121$