How do you evaluate $\sqrt{777924} - \sqrt{\sqrt{31696}} - \sqrt{30 + \sqrt{1156}} + \sqrt{4624}$ $\sqrt { 777924} - \sqrt { \sqrt { 31696} } - \sqrt { 30+ \sqrt { 1156} } + \sqrt { 4624}$ ?

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How do you evaluate $\sqrt{777924} - \sqrt{\sqrt{31696}} - \sqrt{30 + \sqrt{1156}} + \sqrt{4624}$ $\sqrt { 777924} - \sqrt { \sqrt { 31696} } - \sqrt { 30+ \sqrt { 1156} } + \sqrt { 4624}$ ?

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Answer 1 · 2017-02-23T12:40:51

$942 - 2 \sqrt[4]{1981} ≅ 928.657$ $942 - 2\root{4}{1981} ~= 928.657$

Explanation:

I rather use one of "Prime Factorization Calculator" like this one, you can do it yourself but I think it wastes your time.
Let's do it:
$777924 = 2^{2} \cdot 3^{4} \cdot 7^{4} \Rightarrow \sqrt{777924} = 2 \cdot 3^{2} \cdot 7^{2} = 882$ $777924 = 2^2*3^4*7^4 => \sqrt(777924) = 2*3^2*7^2 = 882$

$31696 = 2^{4} \cdot 7 \cdot 283 \Rightarrow \sqrt{\sqrt{31696}} = 2 \sqrt{\sqrt{7 \cdot 283}}$ $31696 = 2^4*7*283 => \sqrt(\sqrt(31696)) = 2\sqrt(\sqrt(7*283))$

$31696 = 2^{4} \cdot 7 \cdot 283 \Rightarrow \sqrt{\sqrt{31696}} = 2 \sqrt{\sqrt{7 \cdot 283}} = 2 \sqrt[4]{1981}$ $31696 = 2^4*7*283 => \sqrt(\sqrt(31696)) = 2\sqrt(\sqrt(7*283)) = 2\root{4}{1981}$

$1156 = 2^{2} \cdot 17^{2} \Rightarrow \sqrt{1156} = 2 \cdot 17 = 34 \Rightarrow \sqrt{30 + \sqrt{1156}} = \sqrt{64} = 8$ $1156 = 2^2*17^2 => \sqrt(1156) = 2*17=34 => \sqrt(30+\sqrt(1156)) = \sqrt(64) = 8$

$4624 = 2^{4} \cdot 17^{2} \Rightarrow \sqrt{4624} = 2^{2} \cdot 17 = 68$ $4624 = 2^4*17^2 => \sqrt(4624) = 2^2*17 = 68$

and answer will be:

$882 - 2 \sqrt[4]{1981} - 8 + 68$ $882 - 2\root{4}{1981} - 8 + 68$
$942 - 2 \sqrt[4]{1981} ≅ 928.657$ $942 - 2\root{4}{1981} ~= 928.657$

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How do you evaluate $\sqrt{777924} - \sqrt{\sqrt{31696}} - \sqrt{30 + \sqrt{1156}} + \sqrt{4624}$ $\sqrt { 777924} - \sqrt { \sqrt { 31696} } - \sqrt { 30+ \sqrt { 1156} } + \sqrt { 4624}$ ?

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How do you evaluate √777924−√√31696−√30+√1156+√4624\sqrt { 777924} - \sqrt { \sqrt { 31696} } - \sqrt { 30+ \sqrt { 1156} } + \sqrt { 4624}?

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How do you evaluate $\sqrt{777924} - \sqrt{\sqrt{31696}} - \sqrt{30 + \sqrt{1156}} + \sqrt{4624}$ $\sqrt { 777924} - \sqrt { \sqrt { 31696} } - \sqrt { 30+ \sqrt { 1156} } + \sqrt { 4624}$ ?