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  4. The value of y such that √188+√53+√y=14 is:

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

Squares and Square Roots and Cubes and Cube Roots

Solution:

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 $
$\therefore y=121$