Simplify ( square root of 560x^3)/( square root of 7x^2)

$\frac{\sqrt{560 x^{3}}}{\sqrt{7 x^{2}}}$

Combine $\sqrt{560 x^{3}}$ and $\sqrt{7 x^{2}}$ into a single radical.

$\sqrt{\frac{560 x^{3}}{7 x^{2}}}$

Reduce the expression $\frac{560 x^{3}}{7 x^{2}}$ by cancelling the common factors.

Factor $7$ out of $560 x^{3}$ .

$\sqrt{\frac{7 (80 x^{3})}{7 x^{2}}}$

Factor $7$ out of $7 x^{2}$ .

$\sqrt{\frac{7 (80 x^{3})}{7 (x^{2})}}$

Cancel the common factor.

$\sqrt{\frac{7 (80 x^{3})}{7 x^{2}}}$

Rewrite the expression.

$\sqrt{\frac{80 x^{3}}{x^{2}}}$

Cancel the common factor of $x^{3}$ and $x^{2}$ .

Factor $x^{2}$ out of $80 x^{3}$ .

$\sqrt{\frac{x^{2} (80 x)}{x^{2}}}$

Cancel the common factors.

Multiply by $1$ .

$\sqrt{\frac{x^{2} (80 x)}{x^{2} \cdot 1}}$

Cancel the common factor.

$\sqrt{\frac{x^{2} (80 x)}{x^{2} \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{80 x}{1}}$

Divide $80 x$ by $1$ .

$\sqrt{80 x}$

Rewrite $80 x$ as ${(2^{2})}^{2} \cdot (5 x)$ .

Factor $16$ out of $80$ .

$\sqrt{16 (5) x}$

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

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

$2^{2} \sqrt{5 x}$

Raise $2$ to the power of $2$ .

$4 \sqrt{5 x}$