Simplify ( square root of 24x^4)/( square root of 3x)

$\frac{\sqrt{24 x^{4}}}{\sqrt{3 x}}$

Step 1

Combine $\sqrt{24 x^{4}}$ and $\sqrt{3 x}$ into a single radical.

$\sqrt{\frac{24 x^{4}}{3 x}}$

Step 2

Reduce the expression $\frac{24 x^{4}}{3 x}$ by cancelling the common factors.

Factor $3$ out of $24 x^{4}$ .

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

Factor $3$ out of $3 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Cancel the common factor of $x^{4}$ and $x$ .

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

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

Cancel the common factors.

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

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

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

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

Cancel the common factor.

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

Rewrite the expression.

$\sqrt{\frac{8 x^{3}}{1}}$

Divide $8 x^{3}$ by $1$ .

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

Step 4

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

Factor $4$ out of $8$ .

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

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

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

Factor out $x^{2}$ .

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

Move $2$ .

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

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

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

Add parentheses.

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

Step 5

Pull terms out from under the radical.

$2 x \sqrt{2 x}$

Simplify ( square root of 24x^4)/( square root of 3x)

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