Algebra Examples

$\frac{4 \sqrt{150}}{\sqrt{189 x}}$

Step 1

Combine $\sqrt{150}$ and $\sqrt{189 x}$ into a single radical.

$4 \sqrt{\frac{150}{189 x}}$

Step 2

Reduce the expression $\frac{150}{189 x}$ by cancelling the common factors.

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Step 2.1

Factor $3$ out of $150$ .

$4 \sqrt{\frac{3 (50)}{189 x}}$

Step 2.2

Factor $3$ out of $189 x$ .

$4 \sqrt{\frac{3 (50)}{3 (63 x)}}$

Step 2.3

Cancel the common factor.

$4 \sqrt{\frac{3 \cdot 50}{3 (63 x)}}$

Step 2.4

Rewrite the expression.

$4 \sqrt{\frac{50}{63 x}}$

Step 3

Rewrite $\frac{50}{63 x}$ as ${(\frac{5}{3})}^{2} \frac{2}{7 x}$ .

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Step 3.1

Factor the perfect power $5^{2}$ out of $50$ .

$4 \sqrt{\frac{5^{2} \cdot 2}{63 x}}$

Step 3.2

Factor the perfect power $3^{2}$ out of $63 x$ .

$4 \sqrt{\frac{5^{2} \cdot 2}{3^{2} \cdot (7 x)}}$

Step 3.3

Rearrange the fraction $\frac{5^{2} \cdot 2}{3^{2} \cdot (7 x)}$ .

$4 \sqrt{{(\frac{5}{3})}^{2} \frac{2}{7 x}}$

Step 4

Pull terms out from under the radical.

$4 (\frac{5}{3} \sqrt{\frac{2}{7 x}})$

Step 5

Rewrite $\sqrt{\frac{2}{7 x}}$ as $\frac{\sqrt{2}}{\sqrt{7 x}}$ .

$4 (\frac{5}{3} \cdot \frac{\sqrt{2}}{\sqrt{7 x}})$

Step 6

Multiply $\frac{\sqrt{2}}{\sqrt{7 x}}$ by $\frac{\sqrt{7 x}}{\sqrt{7 x}}$ .

$4 (\frac{5}{3} (\frac{\sqrt{2}}{\sqrt{7 x}} \cdot \frac{\sqrt{7 x}}{\sqrt{7 x}}))$

Step 7

Combine and simplify the denominator.

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Step 7.1

Multiply $\frac{\sqrt{2}}{\sqrt{7 x}}$ by $\frac{\sqrt{7 x}}{\sqrt{7 x}}$ .

$4 (\frac{5}{3} \cdot \frac{\sqrt{2} \sqrt{7 x}}{\sqrt{7 x} \sqrt{7 x}})$

Step 7.2

Raise $\sqrt{7 x}$ to the power of $1$ .

$4 (\frac{5}{3} \cdot \frac{\sqrt{2} \sqrt{7 x}}{{\sqrt{7 x}}^{1} \sqrt{7 x}})$

Step 7.3

Raise $\sqrt{7 x}$ to the power of $1$ .

$4 (\frac{5}{3} \cdot \frac{\sqrt{2} \sqrt{7 x}}{{\sqrt{7 x}}^{1} {\sqrt{7 x}}^{1}})$

Step 7.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4 (\frac{5}{3} \cdot \frac{\sqrt{2} \sqrt{7 x}}{{\sqrt{7 x}}^{1 + 1}})$

Step 7.5

Add $1$ and $1$ .

$4 (\frac{5}{3} \cdot \frac{\sqrt{2} \sqrt{7 x}}{{\sqrt{7 x}}^{2}})$

Step 7.6

Rewrite ${\sqrt{7 x}}^{2}$ as $7 x$ .

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Step 7.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7 x}$ as ${(7 x)}^{\frac{1}{2}}$ .

$4 (\frac{5}{3} \cdot \frac{\sqrt{2} \sqrt{7 x}}{{({(7 x)}^{\frac{1}{2}})}^{2}})$

Step 7.6.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$4 (\frac{5}{3} \cdot \frac{\sqrt{2} \sqrt{7 x}}{{(7 x)}^{\frac{1}{2} \cdot 2}})$

Step 7.6.3

Combine $\frac{1}{2}$ and $2$ .

$4 (\frac{5}{3} \cdot \frac{\sqrt{2} \sqrt{7 x}}{{(7 x)}^{\frac{2}{2}}})$

Step 7.6.4

Cancel the common factor of $2$ .

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Step 7.6.4.1

Cancel the common factor.

$4 (\frac{5}{3} \cdot \frac{\sqrt{2} \sqrt{7 x}}{{(7 x)}^{\frac{2}{2}}})$

Step 7.6.4.2

Rewrite the expression.

$4 (\frac{5}{3} \cdot \frac{\sqrt{2} \sqrt{7 x}}{{(7 x)}^{1}})$

Step 7.6.5

Simplify.

$4 (\frac{5}{3} \cdot \frac{\sqrt{2} \sqrt{7 x}}{7 x})$

Step 8

Simplify the numerator.

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Step 8.1

Combine using the product rule for radicals.

$4 (\frac{5}{3} \cdot \frac{\sqrt{2 (7 x)}}{7 x})$

Step 8.2

Multiply $2$ by $7$ .

$4 (\frac{5}{3} \cdot \frac{\sqrt{14 x}}{7 x})$

Step 9

Multiply $\frac{5}{3} \cdot \frac{\sqrt{14 x}}{7 x}$ .

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Step 9.1

Multiply $\frac{5}{3}$ by $\frac{\sqrt{14 x}}{7 x}$ .

$4 \frac{5 \sqrt{14 x}}{3 (7 x)}$

Step 9.2

Multiply $7$ by $3$ .

$4 \frac{5 \sqrt{14 x}}{21 x}$

Step 10

Multiply $4 \frac{5 \sqrt{14 x}}{21 x}$ .

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Step 10.1

Combine $4$ and $\frac{5 \sqrt{14 x}}{21 x}$ .

$\frac{4 (5 \sqrt{14 x})}{21 x}$

Step 10.2

Multiply $5$ by $4$ .

$\frac{20 \sqrt{14 x}}{21 x}$