Simplify square root of 54xy^4

$\sqrt{54 x y^{4}}$

Step 1

Rewrite $54 x y^{4}$ as ${(3 y^{2})}^{2} \cdot (6 x)$ .

Factor $9$ out of $54$ .

$\sqrt{9 (6) x y^{4}}$

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} \cdot 6 x y^{4}}$

Rewrite $y^{4}$ as ${(y^{2})}^{2}$ .

$\sqrt{3^{2} \cdot 6 x {(y^{2})}^{2}}$

Move $x$ .

$\sqrt{3^{2} \cdot 6 {(y^{2})}^{2} x}$

Move $6$ .

$\sqrt{3^{2} {(y^{2})}^{2} \cdot 6 x}$

Rewrite $3^{2} {(y^{2})}^{2}$ as ${(3 y^{2})}^{2}$ .

$\sqrt{{(3 y^{2})}^{2} \cdot 6 x}$

Add parentheses.

$\sqrt{{(3 y^{2})}^{2} \cdot (6 x)}$

Step 2

Pull terms out from under the radical.

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