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Question : $\frac{{\sqrt{10+\sqrt{25+\sqrt{108+\sqrt{154+\sqrt{225}}}}}}}{\sqrt[3]{8}}=?$

Option 1: $4$

Option 2: $2$

Option 3: $8$

Option 4: $\frac{1}{2}$


Team Careers360 15th Jan, 2024
Answer (1)
Team Careers360 18th Jan, 2024

Correct Answer: $2$


Solution : Given: $\frac{{\sqrt{10+\sqrt{25+\sqrt{108+\sqrt{154+\sqrt{225}}}}}}}{\sqrt[3]{8}}$
$=\frac{{\sqrt{10+\sqrt{25+\sqrt{108+\sqrt{154+15}}}}}}{2}$
$= \frac{{\sqrt{10+\sqrt{25+\sqrt{108+\sqrt{169}}}}}}{2}$
$= \frac{{\sqrt{10+\sqrt{25+\sqrt{108+13}}}}}{2}$
$= \frac{{\sqrt{10+\sqrt{25+\sqrt{121}}}}}{2}$
$= \frac{{\sqrt{10+\sqrt{25+11}}}}{2}$
$=\frac{{\sqrt{10+\sqrt{36}}}}{2}$
$= \frac{{\sqrt{10+6}}}{2}$
$=\frac{{\sqrt{16}}}{2}$
$= \frac{4}{2}$
$= 2$
Hence, the correct answer is $2$.

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