# How do you simplify sqrt(54xy^4)?

Jul 7, 2016

$\sqrt{54 x {y}^{4}} = \sqrt{{6.3}^{2} \cdot x {\left({y}^{2}\right)}^{2}} = 3 {y}^{2} \sqrt{6 x}$

#### Explanation:

$\sqrt{54 x {y}^{4}} = \sqrt{{6.3}^{2} \cdot x {\left({y}^{2}\right)}^{2}} = 3 {y}^{2} \sqrt{6 x}$

Find the perfect squares and break them out to eventually get to $3 {y}^{2} \sqrt{6 x}$

#### Explanation:

To solve this, we're going to be looking for squares under the square root sign. Once we find them, we'll separate them out and take the root, while the rest will stay within. Like this:

Starting with the original:

$\sqrt{54 x y 4}$

Let's do the variables first. We know that $x$ term is not a square, so we don't need to do anything with it. The $y$ term, however, consists of 2 squares, so we'll separate them out.

Now to the number 54. $54 = 9 \cdot 6$ and 9 is a perfect square.

Let's take the original and break out the perfect squares:

$\sqrt{\left(9\right) \left(6\right) \left(x\right) \left({y}^{2}\right) \left({y}^{2}\right)}$

we can rewrite this as:

$\sqrt{9} \sqrt{{y}^{2}} \sqrt{{y}^{2}} \sqrt{6 x}$

now let's take the square roots of the perfect squares:

$3 \left(y\right) \left(y\right) \sqrt{6 x}$

and we can clean this up by combining the two y terms:

$3 {y}^{2} \sqrt{6 x}$