Simplify ( square root of 12x^8)/( square root of 3x^2)

$\frac{\sqrt{12 x^{8}}}{\sqrt{3 x^{2}}}$

Step 1

Combine $\sqrt{12 x^{8}}$ and $\sqrt{3 x^{2}}$ into a single radical.

$\sqrt{\frac{12 x^{8}}{3 x^{2}}}$

Step 2

Reduce the expression $\frac{12 x^{8}}{3 x^{2}}$ by cancelling the common factors.

Factor $3$ out of $12 x^{8}$ .

$\sqrt{\frac{3 (4 x^{8})}{3 x^{2}}}$

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

$\sqrt{\frac{3 (4 x^{8})}{3 (x^{2})}}$

Cancel the common factor.

$\sqrt{\frac{3 (4 x^{8})}{3 x^{2}}}$

Rewrite the expression.

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

Step 3

Cancel the common factor of $x^{8}$ and $x^{2}$ .

Factor $x^{2}$ out of $4 x^{8}$ .

$\sqrt{\frac{x^{2} (4 x^{6})}{x^{2}}}$

Cancel the common factors.

Multiply by $1$ .

$\sqrt{\frac{x^{2} (4 x^{6})}{x^{2} \cdot 1}}$

Cancel the common factor.

$\sqrt{\frac{x^{2} (4 x^{6})}{x^{2} \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{4 x^{6}}{1}}$

Divide $4 x^{6}$ by $1$ .

$\sqrt{4 x^{6}}$

Step 4

Rewrite $4 x^{6}$ as ${(2 x^{3})}^{2}$ .

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

Step 5

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

$2 x^{3}$