Question

If $\sqrt{10+\sqrt{25+\sqrt{x+\sqrt{154+\sqrt{225}}}}}=4$ find the value of $x$

• A. 110
• B. 108
• C. 100
• D. 114

Answer 1

Answer: (B)

108

We have,

$\sqrt{10+\sqrt{25+\sqrt{x+\sqrt{154+\sqrt{225}}}}}=4$

$\Rightarrow \sqrt{10+\sqrt{25+\sqrt{x+\sqrt{154+15}}}}=4$

$\Rightarrow \sqrt{10+\sqrt{25+\sqrt{x+\sqrt{169}}}}=4$

$\Rightarrow \sqrt{10+\sqrt{25+\sqrt{x+13}}}=4$

On squaring both sides, we get

$10+\sqrt{25+\sqrt{x+13}}=16$

$\sqrt{25+\sqrt{x+13}}=6$

On squaring both sides, we get

$25+\sqrt{x+13}=36$

$\Rightarrow \sqrt{x+13}=11$

On squaring both sides, we get

$x+13=121$

$x=121-13=108$

Hence, $x=108$