Question

$\sqrt{10 + \sqrt{25 + \sqrt{108 + \sqrt{169} } } }$
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Answer 1

Answer :-

The answer is 4 .

Step-by-step-Explaination :-

$\rm\sqrt{10 + \sqrt{25 + \sqrt{108 + \sqrt{169} } } }$

$\rm \longmapsto \sqrt{10 + \sqrt{25 + \sqrt{108 \sqrt{13 \times 13} } } }$

$\rm \longmapsto \sqrt{10 + \sqrt{25 + \sqrt{108 + 13} } }$

$\rm \longmapsto \sqrt{10 + \sqrt{25 + \sqrt{121} } }$

$\rm \longmapsto \sqrt{10 + \sqrt{25 + \sqrt{11 \times 11} } }$

$\rm \longmapsto \sqrt{10 + \sqrt{25 + 11 } }$

$\rm \longmapsto \sqrt{10 + \sqrt{36 } }$

$\rm \longmapsto \sqrt{10 + \sqrt{6 \times 6} }$

$\rm \longmapsto \sqrt{10 +6 }$

$\rightarrow \sqrt{16}$

$\rightarrow \sqrt{4 \times 4}$

$\rightarrow 4$