# How do you simplify sqrt(63w^36)?

Jul 15, 2017

$3 \sqrt{7} \cdot {w}^{18} = 3 {w}^{18} \sqrt{7}$

#### Explanation:

$\sqrt{63 {w}^{36}} = \sqrt{63} \cdot \sqrt{{w}^{36}}$

$\sqrt{{w}^{36}} = {\left({w}^{36}\right)}^{\frac{1}{2}} = {w}^{\frac{36}{2}} = {w}^{18}$

$\sqrt{63} = \sqrt{a \cdot b}$, where a nd b are factors of 63, and one is a perfect square number.

Two factors of 63 are 9 and 7.

$\sqrt{63} = \sqrt{9 \cdot 7} = \sqrt{9} \cdot \sqrt{7} = 3 \sqrt{7}$.

As $\sqrt{63 {w}^{36}} = \sqrt{63} \cdot \sqrt{{w}^{36}}$, and we calculated thise vakues, it is just $3 {w}^{18} \sqrt{7}$