Simplify ( square root of 48x^7y^5)/( square root of x^2)

$\frac{\sqrt{48 x^{7} y^{5}}}{\sqrt{x^{2}}}$

Step 1

Combine $\sqrt{48 x^{7} y^{5}}$ and $\sqrt{x^{2}}$ into a single radical.

$\sqrt{\frac{48 x^{7} y^{5}}{x^{2}}}$

Step 2

Reduce the expression by cancelling the common factors.

Reduce the expression $\frac{48 x^{7} y^{5}}{x^{2}}$ by cancelling the common factors.

Factor $x^{2}$ out of $48 x^{7} y^{5}$ .

$\sqrt{\frac{x^{2} (48 x^{5} y^{5})}{x^{2}}}$

Multiply by $1$ .

$\sqrt{\frac{x^{2} (48 x^{5} y^{5})}{x^{2} \cdot 1}}$

Cancel the common factor.

$\sqrt{\frac{x^{2} (48 x^{5} y^{5})}{x^{2} \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{48 x^{5} y^{5}}{1}}$

Divide $48 x^{5} y^{5}$ by $1$ .

$\sqrt{48 x^{5} y^{5}}$

Step 3

Rewrite $48 x^{5} y^{5}$ as ${(4 x^{2} y^{2})}^{2} \cdot (3 x y)$ .

Factor $16$ out of $48$ .

$\sqrt{16 (3) x^{5} y^{5}}$

Rewrite $16$ as $4^{2}$ .

$\sqrt{4^{2} \cdot 3 x^{5} y^{5}}$

Factor out $x^{4}$ .

$\sqrt{4^{2} \cdot 3 (x^{4} x) y^{5}}$

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

$\sqrt{4^{2} \cdot 3 ({(x^{2})}^{2} x) y^{5}}$

Factor out $y^{4}$ .

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

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

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

Move $x$ .

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

Move $3$ .

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

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

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

Add parentheses.

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

Add parentheses.

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

Step 4

Pull terms out from under the radical.

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