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

Feb 23, 2017

$942 - 2 \setminus \sqrt[4]{1981} \cong 928.657$

#### 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:
$777924 = {2}^{2} \cdot {3}^{4} \cdot {7}^{4} \implies \setminus \sqrt{777924} = 2 \cdot {3}^{2} \cdot {7}^{2} = 882$

$31696 = {2}^{4} \cdot 7 \cdot 283 \implies \setminus \sqrt{\setminus \sqrt{31696}} = 2 \setminus \sqrt{\setminus \sqrt{7 \cdot 283}}$

$31696 = {2}^{4} \cdot 7 \cdot 283 \implies \setminus \sqrt{\setminus \sqrt{31696}} = 2 \setminus \sqrt{\setminus \sqrt{7 \cdot 283}} = 2 \setminus \sqrt[4]{1981}$

$1156 = {2}^{2} \cdot {17}^{2} \implies \setminus \sqrt{1156} = 2 \cdot 17 = 34 \implies \setminus \sqrt{30 + \setminus \sqrt{1156}} = \setminus \sqrt{64} = 8$

$4624 = {2}^{4} \cdot {17}^{2} \implies \setminus \sqrt{4624} = {2}^{2} \cdot 17 = 68$

$882 - 2 \setminus \sqrt[4]{1981} - 8 + 68$
$942 - 2 \setminus \sqrt[4]{1981} \cong 928.657$