# How do you simplify sqrt(504)?

Jan 10, 2016

$6 \sqrt{14}$

#### Explanation:

First step for simplification in roots is to find the prime factors of the number.

Here factors of 504 are (You can get them by Prime Factorization)

$504 = {2}^{3} \times {3}^{2} \times 7$

$504 = {\left(2 \times 3\right)}^{2} \times 2 \times 7$

$\sqrt{504} = \sqrt{{\left(2 \times 3\right)}^{2} \times 2 \times 7}$

$\sqrt{504} = \left(2 \times 3\right) \sqrt{2 \times 7}$

$\sqrt{504} = 6 \sqrt{14}$

$A \mathrm{dd} i t i o n a l$: Now let me ask you another question (to strengthen your concepts)

What minimum positive number should you multiply with 504 so that the new number is a perfect square??