Question

If $\sqrt{10+\sqrt{25+\sqrt{108+\sqrt{169}}}}=x$, then value of $x$ is

• A. $4$
• B. $6$
• C. $8$
• D. $10$

Answer 1

The correct option is A $4$

$\sqrt{10+\sqrt{25+\sqrt{108+\sqrt{169}}}}=x$

$\Rightarrow$ $\sqrt{10+\sqrt{25+\sqrt{108+13}}}=x$

$\Rightarrow$ $\sqrt{10+\sqrt{25+\sqrt{121}}}=x$

$\Rightarrow$ $\sqrt{10+\sqrt{25+11}}=x$

$\Rightarrow$ $\sqrt{10+\sqrt{36}}=x$

$\Rightarrow$ $\sqrt{10+6}=x$

$\Rightarrow$ $\sqrt{16}=x$

$\therefore$ $x=4$