Divide (20 square root of 45x^4)/(4 square root of 9x)

$\frac{20 \sqrt{45 x^{4}}}{4 \sqrt{9 x}}$

Step 1

Cancel the common factor of $20$ and $4$ .

Factor $4$ out of $20 \sqrt{45 x^{4}}$ .

$\frac{4 (5 \sqrt{45 x^{4}})}{4 \sqrt{9 x}}$

Cancel the common factors.

Factor $4$ out of $4 \sqrt{9 x}$ .

$\frac{4 (5 \sqrt{45 x^{4}})}{4 (\sqrt{9 x})}$

Cancel the common factor.

$\frac{4 (5 \sqrt{45 x^{4}})}{4 \sqrt{9 x}}$

Rewrite the expression.

$\frac{5 \sqrt{45 x^{4}}}{\sqrt{9 x}}$

Step 2

Combine $\sqrt{45 x^{4}}$ and $\sqrt{9 x}$ into a single radical.

$5 \sqrt{\frac{45 x^{4}}{9 x}}$

Step 3

Reduce the expression $\frac{45 x^{4}}{9 x}$ by cancelling the common factors.

Factor $9$ out of $45 x^{4}$ .

$5 \sqrt{\frac{9 (5 x^{4})}{9 x}}$

Factor $9$ out of $9 x$ .

$5 \sqrt{\frac{9 (5 x^{4})}{9 (x)}}$

Cancel the common factor.

$5 \sqrt{\frac{9 (5 x^{4})}{9 x}}$

Rewrite the expression.

$5 \sqrt{\frac{5 x^{4}}{x}}$

Step 4

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

Factor $x$ out of $5 x^{4}$ .

$5 \sqrt{\frac{x (5 x^{3})}{x}}$

Cancel the common factors.

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

$5 \sqrt{\frac{x (5 x^{3})}{x^{1}}}$

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

$5 \sqrt{\frac{x (5 x^{3})}{x \cdot 1}}$

Cancel the common factor.

$5 \sqrt{\frac{x (5 x^{3})}{x \cdot 1}}$

Rewrite the expression.

$5 \sqrt{\frac{5 x^{3}}{1}}$

Divide $5 x^{3}$ by $1$ .

$5 \sqrt{5 x^{3}}$

Step 5

Rewrite $5 x^{3}$ as $x^{2} \cdot (5 x)$ .

Factor out $x^{2}$ .

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

Reorder $5$ and $x^{2}$ .

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

Add parentheses.

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

Step 6

Pull terms out from under the radical.

$5 x \sqrt{5 x}$

Divide (20 square root of 45x^4)/(4 square root of 9x)

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