Simplify ( square root of 125x^6)/( square root of x)

$\frac{\sqrt{125 x^{6}}}{\sqrt{x}}$

Step 1

Combine $\sqrt{125 x^{6}}$ and $\sqrt{x}$ into a single radical.

$\sqrt{\frac{125 x^{6}}{x}}$

Step 2

Reduce the expression by cancelling the common factors.

Reduce the expression $\frac{125 x^{6}}{x}$ by cancelling the common factors.

Factor $x$ out of $125 x^{6}$ .

$\sqrt{\frac{x (125 x^{5})}{x}}$

Raise $x$ to the power of $1$ .

$\sqrt{\frac{x (125 x^{5})}{x^{1}}}$

Factor $x$ out of $x^{1}$ .

$\sqrt{\frac{x (125 x^{5})}{x \cdot 1}}$

Cancel the common factor.

$\sqrt{\frac{x (125 x^{5})}{x \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{125 x^{5}}{1}}$

Divide $125 x^{5}$ by $1$ .

$\sqrt{125 x^{5}}$

Step 3

Rewrite $125 x^{5}$ as ${(5 x^{2})}^{2} \cdot (5 x)$ .

Factor $25$ out of $125$ .

$\sqrt{25 (5) x^{5}}$

Rewrite $25$ as $5^{2}$ .

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

Factor out $x^{4}$ .

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

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

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

Move $5$ .

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

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

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

Add parentheses.

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

Step 4

Pull terms out from under the radical.

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