Algebra Examples

$\sqrt{\frac{140 x^{3}}{5 x}}$

Step 1

Reduce the expression $\frac{140 x^{3}}{5 x}$ by cancelling the common factors.

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Step 1.1

Factor $5$ out of $140 x^{3}$ .

$\sqrt{\frac{5 (28 x^{3})}{5 x}}$

Step 1.2

Factor $5$ out of $5 x$ .

$\sqrt{\frac{5 (28 x^{3})}{5 (x)}}$

Step 1.3

Cancel the common factor.

$\sqrt{\frac{5 (28 x^{3})}{5 x}}$

Step 1.4

Rewrite the expression.

$\sqrt{\frac{28 x^{3}}{x}}$

$\sqrt{\frac{28 x^{3}}{x}}$

Step 2

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

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Step 2.1

Factor $x$ out of $28 x^{3}$ .

$\sqrt{\frac{x (28 x^{2})}{x}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

$\sqrt{\frac{x (28 x^{2})}{x^{1}}}$

Step 2.2.2

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

$\sqrt{\frac{x (28 x^{2})}{x \cdot 1}}$

Step 2.2.3

Cancel the common factor.

$\sqrt{\frac{x (28 x^{2})}{x \cdot 1}}$

Step 2.2.4

Rewrite the expression.

$\sqrt{\frac{28 x^{2}}{1}}$

Step 2.2.5

Divide $28 x^{2}$ by $1$ .

$\sqrt{28 x^{2}}$

$\sqrt{28 x^{2}}$

$\sqrt{28 x^{2}}$

Step 3

Rewrite $28 x^{2}$ as ${(2 x)}^{2} \cdot 7$ .

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Step 3.1

Factor $4$ out of $28$ .

$\sqrt{4 (7) x^{2}}$

Step 3.2

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

$\sqrt{2^{2} \cdot 7 x^{2}}$

Step 3.3

Move $7$ .

$\sqrt{2^{2} x^{2} \cdot 7}$

Step 3.4

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

$\sqrt{{(2 x)}^{2} \cdot 7}$

$\sqrt{{(2 x)}^{2} \cdot 7}$

Step 4

Pull terms out from under the radical.

$2 x \sqrt{7}$

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