How do you simplify sqrt(1176)?

Feb 13, 2016

$1176 = 14 \sqrt{6}$

Explanation:

Start by writing the prime factorization of $1176$.

$1176 = {2}^{3} \times 3 \times {7}^{2}$

Then take the square root

$\sqrt{1176} = \sqrt{{2}^{3}} \times \sqrt{3} \times \sqrt{{7}^{2}}$

$= {\sqrt{2}}^{3} \times \sqrt{3} \times 7$

$= 2 \sqrt{2} \times \sqrt{3} \times 7$

$= \left(2 \times 7\right) \times \sqrt{2 \times 3}$

$= 14 \sqrt{6}$