Question

Find the value of √ 1+9√ 9+10√11+ √5+5√16

Answer 1

$The \: value \: of \: \sqrt{1+9\sqrt{9+10\sqrt{11+\sqrt{5+5\sqrt{16}}}}}$

$= \sqrt{1+9\sqrt{9+10\sqrt{11+\sqrt{5+5\times 4}}}}$

$= \sqrt{1+9\sqrt{9+10\sqrt{11+\sqrt{5+20}}}}$

$= \sqrt{1+9\sqrt{9+10\sqrt{11+\sqrt{25}}}}$

$= \sqrt{1+9\sqrt{9+10\sqrt{11+5}}}$

$= \sqrt{1+9\sqrt{9+10\sqrt{16}}}$

$= \sqrt{1+9\sqrt{9+10\times 4}}$

$= \sqrt{1+9\sqrt{9+40}}$

$= \sqrt{1+9\sqrt{49}}$

$= \sqrt{1+9\times 7}$

$= \sqrt{1+63}$

$= \sqrt{64}$

$= 8$

Therefore.,

$\red{ The \: value \: of \: \sqrt{1+9\sqrt{9+10\sqrt{11+\sqrt{5+5\sqrt{16}}}}}}$

$\green { = 8}$

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