Simplify ( square root of 80x^4)/( square root of 5x^3)

$\frac{\sqrt{80 x^{4}}}{\sqrt{5 x^{3}}}$

Step 1

Combine $\sqrt{80 x^{4}}$ and $\sqrt{5 x^{3}}$ into a single radical.

$\sqrt{\frac{80 x^{4}}{5 x^{3}}}$

Step 2

Reduce the expression $\frac{80 x^{4}}{5 x^{3}}$ by cancelling the common factors.

Factor $5$ out of $80 x^{4}$ .

$\sqrt{\frac{5 (16 x^{4})}{5 x^{3}}}$

Factor $5$ out of $5 x^{3}$ .

$\sqrt{\frac{5 (16 x^{4})}{5 (x^{3})}}$

Cancel the common factor.

$\sqrt{\frac{5 (16 x^{4})}{5 x^{3}}}$

Rewrite the expression.

$\sqrt{\frac{16 x^{4}}{x^{3}}}$

Step 3

Cancel the common factor of $x^{4}$ and $x^{3}$ .

Factor $x^{3}$ out of $16 x^{4}$ .

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

Cancel the common factors.

Multiply by $1$ .

$\sqrt{\frac{x^{3} (16 x)}{x^{3} \cdot 1}}$

Cancel the common factor.

$\sqrt{\frac{x^{3} (16 x)}{x^{3} \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{16 x}{1}}$

Divide $16 x$ by $1$ .

$\sqrt{16 x}$

Step 4

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

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

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

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

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

Step 5

Pull terms out from under the radical.

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

Step 6

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

$4 \sqrt{x}$