Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

Cancel the common factors.

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Step 1.2.1

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

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

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

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

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

Step 2

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

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Factor $12$ out of $12 x$ .

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

Step 3.3

Cancel the common factor.

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

Step 3.4

Rewrite the expression.

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

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

Step 4

Cancel the common factor of $x^{5}$ and $x$ .

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Step 4.1

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

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

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

Step 4.2.2

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

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

Step 4.2.3

Cancel the common factor.

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

Step 4.2.4

Rewrite the expression.

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

Step 4.2.5

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

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

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

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

Step 5

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

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Step 5.1

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

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

Step 5.2

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

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

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

Step 6

Pull terms out from under the radical.

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

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$