# What is the square root of 7744?

Sep 18, 2015

$\sqrt{7744} = 88$

#### Explanation:

Find prime factors of $7744$:

$7744 = 2 \cdot 3872 = {2}^{2} \cdot 1936 = {2}^{3} \cdot 968 = {2}^{4} \cdot 484$

$= {2}^{5} \cdot 242 = {2}^{6} \cdot 121 = {2}^{6} \cdot 11 \cdot 11$

$= \left({2}^{3} \cdot 11\right) \cdot \left({2}^{3} \cdot 11\right) = {\left({2}^{3} \cdot 11\right)}^{2} = {88}^{2}$

So $\sqrt{7744} = 88$