Simplify the Radical Expression ( square root of 48x^9)/( square root of 6x^3)

$\frac{\sqrt{48 x^{9}}}{\sqrt{6 x^{3}}}$

Step 1

Combine $\sqrt{48 x^{9}}$ and $\sqrt{6 x^{3}}$ into a single radical.

$\sqrt{\frac{48 x^{9}}{6 x^{3}}}$

Step 2

Reduce the expression $\frac{48 x^{9}}{6 x^{3}}$ by cancelling the common factors.

Factor $6$ out of $48 x^{9}$ .

$\sqrt{\frac{6 (8 x^{9})}{6 x^{3}}}$

Factor $6$ out of $6 x^{3}$ .

$\sqrt{\frac{6 (8 x^{9})}{6 (x^{3})}}$

Cancel the common factor.

$\sqrt{\frac{6 (8 x^{9})}{6 x^{3}}}$

Rewrite the expression.

$\sqrt{\frac{8 x^{9}}{x^{3}}}$

Step 3

Cancel the common factor of $x^{9}$ and $x^{3}$ .

Factor $x^{3}$ out of $8 x^{9}$ .

$\sqrt{\frac{x^{3} (8 x^{6})}{x^{3}}}$

Cancel the common factors.

Multiply by $1$ .

$\sqrt{\frac{x^{3} (8 x^{6})}{x^{3} \cdot 1}}$

Cancel the common factor.

$\sqrt{\frac{x^{3} (8 x^{6})}{x^{3} \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{8 x^{6}}{1}}$

Divide $8 x^{6}$ by $1$ .

$\sqrt{8 x^{6}}$

Step 4

Rewrite $8 x^{6}$ as ${(2 x^{3})}^{2} \cdot 2$ .

Factor $4$ out of $8$ .

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

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

$\sqrt{2^{2} \cdot 2 x^{6}}$

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

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

Move $2$ .

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

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

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

Step 5

Pull terms out from under the radical.

$| 2 x^{3} | \sqrt{2}$

Step 6

Remove non-negative terms from the absolute value.

$2 | x^{3} | \sqrt{2}$