Simplify the Radical Expression ( square root of 48x^3)/( square root of 3xy^2)

$\frac{\sqrt{48 x^{3}}}{\sqrt{3 x y^{2}}}$

Step 1

Combine $\sqrt{48 x^{3}}$ and $\sqrt{3 x y^{2}}$ into a single radical.

$\sqrt{\frac{48 x^{3}}{3 x y^{2}}}$

Step 2

Reduce the expression $\frac{48 x^{3}}{3 x y^{2}}$ by cancelling the common factors.

Factor $3$ out of $48 x^{3}$ .

$\sqrt{\frac{3 (16 x^{3})}{3 x y^{2}}}$

Factor $3$ out of $3 x y^{2}$ .

$\sqrt{\frac{3 (16 x^{3})}{3 (x y^{2})}}$

Cancel the common factor.

$\sqrt{\frac{3 (16 x^{3})}{3 (x y^{2})}}$

Rewrite the expression.

$\sqrt{\frac{16 x^{3}}{x y^{2}}}$

Step 3

Cancel the common factor of $x^{3}$ and $x$ .

Factor $x$ out of $16 x^{3}$ .

$\sqrt{\frac{x (16 x^{2})}{x y^{2}}}$

Cancel the common factors.

Factor $x$ out of $x y^{2}$ .

$\sqrt{\frac{x (16 x^{2})}{x (y^{2})}}$

Cancel the common factor.

$\sqrt{\frac{x (16 x^{2})}{x y^{2}}}$

Rewrite the expression.

$\sqrt{\frac{16 x^{2}}{y^{2}}}$

Step 4

Rewrite $16 x^{2}$ as ${(4 x)}^{2}$ .

$\sqrt{\frac{{(4 x)}^{2}}{y^{2}}}$

Step 5

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

$\sqrt{{(\frac{4 x}{y})}^{2}}$

Step 6

Pull terms out from under the radical.

$| \frac{4 x}{y} |$

Step 7

Remove non-negative terms from the absolute value.

$\frac{4 | x |}{| y |}$