Question

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Answer 1

Question :-

$\sf \sqrt{221 + \sqrt{8+ \sqrt{59+ \sqrt{22 + \sqrt{9}}}}}$

Answer :-

$\implies\sf \sqrt{221 + \sqrt{8+ \sqrt{59+ \sqrt{22 + \sqrt{9}}}}}$

• $\sf \sqrt{9} = \sqrt{3\times 3} = 3$

$\implies\sf \sqrt{221 + \sqrt{8+ \sqrt{59+ \sqrt{22 + 3}}}}$

$\implies\sf \sqrt{221 + \sqrt{8+ \sqrt{59+ \sqrt{25}}}}$

• $\sf \sqrt{25} = \sqrt{5\times 5} = 5$

$\implies\sf \sqrt{221 + \sqrt{8+ \sqrt{59+ 5}}}$

$\implies\sf \sqrt{221 + \sqrt{8+ \sqrt{64}}}$

• $\sf \sqrt{64} = \sqrt{8\times8} = 8$

$\implies\sf \sqrt{221 + \sqrt{8+8}}$

$\implies\sf \sqrt{221 + \sqrt{16}}$

• $\sf \sqrt{16} = \sqrt{4\times 4} = 4$

$\implies\sf \sqrt{221 + 4}$

$\implies\sf \sqrt{225}$

$\implies\sf \sqrt{15\times 15}$

$\implies\sf 15$

$\boxed{\sf \sqrt{221 + \sqrt{8+ \sqrt{59+ \sqrt{22 + \sqrt{9}}}}} = 15}$

Answer 2

Answer:

the answer will be 33.660573798.

you can check the answer in calculator.