Algebra Examples

$\frac{\sqrt{150 x^{4}}}{\sqrt{3 x}}$

Step 1

Combine $\sqrt{150 x^{4}}$ and $\sqrt{3 x}$ into a single radical.

$\sqrt{\frac{150 x^{4}}{3 x}}$

Step 2

Reduce the expression $\frac{150 x^{4}}{3 x}$ by cancelling the common factors.

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Step 2.1

Factor $3$ out of $150 x^{4}$ .

$\sqrt{\frac{3 (50 x^{4})}{3 x}}$

Step 2.2

Factor $3$ out of $3 x$ .

$\sqrt{\frac{3 (50 x^{4})}{3 (x)}}$

Step 2.3

Cancel the common factor.

$\sqrt{\frac{3 (50 x^{4})}{3 x}}$

Step 2.4

Rewrite the expression.

$\sqrt{\frac{50 x^{4}}{x}}$

Step 3

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

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Step 3.1

Factor $x$ out of $50 x^{4}$ .

$\sqrt{\frac{x (50 x^{3})}{x}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

$\sqrt{\frac{x (50 x^{3})}{x^{1}}}$

Step 3.2.2

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

$\sqrt{\frac{x (50 x^{3})}{x \cdot 1}}$

Step 3.2.3

Cancel the common factor.

$\sqrt{\frac{x (50 x^{3})}{x \cdot 1}}$

Step 3.2.4

Rewrite the expression.

$\sqrt{\frac{50 x^{3}}{1}}$

Step 3.2.5

Divide $50 x^{3}$ by $1$ .

$\sqrt{50 x^{3}}$

Step 4

Rewrite $50 x^{3}$ as ${(5 x)}^{2} \cdot (2 x)$ .

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Step 4.1

Factor $25$ out of $50$ .

$\sqrt{25 (2) x^{3}}$

Step 4.2

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2} \cdot 2 x^{3}}$

Step 4.3

Factor out $x^{2}$ .

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

Step 4.4

Move $2$ .

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

Step 4.5

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

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

Step 4.6

Add parentheses.

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

Step 5

Pull terms out from under the radical.

$5 x \sqrt{2 x}$