ABC26GN1335 · Square Roots and Cube Roots

Subject: General Aptitude · Chapter: Square Roots and Cube Roots · Exam: · Marks: · Difficulty:

The value of $\sqrt{10+\sqrt{25+\sqrt{108+\sqrt{154+\sqrt{225}}}}}$ is
(a)4
(b)6
(c)8
(d)10
Answer
Answer (as printed): A
Explanation
Given exp. $$\begin{aligned} & =\sqrt{10+\sqrt{25+\sqrt{108+\sqrt{154+15}}}} \\ & =\sqrt{10+\sqrt{25+\sqrt{108+\sqrt{169}}}} \\ & =\sqrt{10+\sqrt{25+\sqrt{108+13}}} \\ & =\sqrt{10+\sqrt{25+\sqrt{121}}} \\ & =\sqrt{10+\sqrt{25+11}}=\sqrt{10+\sqrt{36}} \\ & =\sqrt{10+6}=\sqrt{16}=4 . \end{aligned}$$

Explanation as extracted from the printed page; notation may be imperfect.

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