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

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

Step 1

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

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

Step 2

Reduce the expression by cancelling the common factors.

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

Factor $x^{3}$ out of $80 x^{5}$ .

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

Multiply by $1$ .

$\sqrt{\frac{x^{3} (80 x^{2})}{x^{3} \cdot 1}}$

Cancel the common factor.

$\sqrt{\frac{x^{3} (80 x^{2})}{x^{3} \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{80 x^{2}}{1}}$

Divide $80 x^{2}$ by $1$ .

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

Step 3

Rewrite $80 x^{2}$ as ${(4 x)}^{2} \cdot 5$ .

Factor $16$ out of $80$ .

$\sqrt{16 (5) x^{2}}$

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

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

Move $5$ .

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

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

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

Step 4

Pull terms out from under the radical.

$4 x \sqrt{5}$