Simplify: $\sqrt{110+\sqrt{121}}$.

Given: $\sqrt{110+\sqrt{121}}$.

To do: To simplify: $\sqrt{110+\sqrt{121}}$.

Solution:

$\sqrt{110+\sqrt{121}}$

$=\sqrt{110+\sqrt{11\times11}}$                             [$\because 121=11\times11$]

$=\sqrt{110+11}$

$=\sqrt{121}$

$=\sqrt{11\times11}$

$=11$

Thus, $\sqrt{110+\sqrt{121}}=11$.

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Updated on: 10-Oct-2022

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