Simplify (15 square root of 60x^5)/(3 square root of 12x)

$\frac{15 \sqrt{60 x^{5}}}{3 \sqrt{12 x}}$

Cancel the common factor of $15$ and $3$ .

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Factor $3$ out of $15 \sqrt{60 x^{5}}$ .

$\frac{3 (5 \sqrt{60 x^{5}})}{3 \sqrt{12 x}}$

Cancel the common factors.

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Factor $3$ out of $3 \sqrt{12 x}$ .

$\frac{3 (5 \sqrt{60 x^{5}})}{3 (\sqrt{12 x})}$

Cancel the common factor.

$\frac{3 (5 \sqrt{60 x^{5}})}{3 \sqrt{12 x}}$

Rewrite the expression.

$\frac{5 \sqrt{60 x^{5}}}{\sqrt{12 x}}$

Combine $\sqrt{60 x^{5}}$ and $\sqrt{12 x}$ into a single radical.

$5 \sqrt{\frac{60 x^{5}}{12 x}}$

Reduce the expression $\frac{60 x^{5}}{12 x}$ by cancelling the common factors.

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Factor $12$ out of $60 x^{5}$ .

$5 \sqrt{\frac{12 (5 x^{5})}{12 x}}$

Factor $12$ out of $12 x$ .

$5 \sqrt{\frac{12 (5 x^{5})}{12 (x)}}$

Cancel the common factor.

$5 \sqrt{\frac{12 (5 x^{5})}{12 x}}$

Rewrite the expression.

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

Reduce the expression by cancelling the common factors.

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Reduce the expression $\frac{5 x^{5}}{x}$ by cancelling the common factors.

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

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

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

$5 \sqrt{\frac{x (5 x^{4})}{x^{1}}}$

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

$5 \sqrt{\frac{x (5 x^{4})}{x \cdot 1}}$

Cancel the common factor.

$5 \sqrt{\frac{x (5 x^{4})}{x \cdot 1}}$

Rewrite the expression.

$5 \sqrt{\frac{5 x^{4}}{1}}$

Divide $5 x^{4}$ by $1$ .

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

Rewrite $5 x^{4}$ as ${(x^{2})}^{2} \cdot 5$ .

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

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

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

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

Pull terms out from under the radical.

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

Simplify (15 square root of 60x^5)/(3 square root of 12x)