Simplify (2 square root of 52x^9)/( square root of 13x)

$\frac{2 \sqrt{52 x^{9}}}{\sqrt{13 x}}$

Step 1

Combine $\sqrt{52 x^{9}}$ and $\sqrt{13 x}$ into a single radical.

$2 \sqrt{\frac{52 x^{9}}{13 x}}$

Step 2

Reduce the expression $\frac{52 x^{9}}{13 x}$ by cancelling the common factors.

Factor $13$ out of $52 x^{9}$ .

$2 \sqrt{\frac{13 (4 x^{9})}{13 x}}$

Factor $13$ out of $13 x$ .

$2 \sqrt{\frac{13 (4 x^{9})}{13 (x)}}$

Cancel the common factor.

$2 \sqrt{\frac{13 (4 x^{9})}{13 x}}$

Rewrite the expression.

$2 \sqrt{\frac{4 x^{9}}{x}}$

Step 3

Cancel the common factor of $x^{9}$ and $x$ .

Factor $x$ out of $4 x^{9}$ .

$2 \sqrt{\frac{x (4 x^{8})}{x}}$

Cancel the common factors.

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

$2 \sqrt{\frac{x (4 x^{8})}{x^{1}}}$

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

$2 \sqrt{\frac{x (4 x^{8})}{x \cdot 1}}$

Cancel the common factor.

$2 \sqrt{\frac{x (4 x^{8})}{x \cdot 1}}$

Rewrite the expression.

$2 \sqrt{\frac{4 x^{8}}{1}}$

Divide $4 x^{8}$ by $1$ .

$2 \sqrt{4 x^{8}}$

Step 4

Rewrite $4 x^{8}$ as ${(2 x^{4})}^{2}$ .

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

Step 5

Pull terms out from under the radical, assuming positive real numbers.

$2 (2 x^{4})$

Step 6

Multiply $2$ by $2$ .

$4 x^{4}$