Algebra Examples

$\frac{3 \sqrt{160}}{\sqrt{1350 x}}$

Step 1

Combine $\sqrt{160}$ and $\sqrt{1350 x}$ into a single radical.

$3 \sqrt{\frac{160}{1350 x}}$

Step 2

Reduce the expression $\frac{160}{1350 x}$ by cancelling the common factors.

Tap for more steps...

Step 2.1

Factor $10$ out of $160$ .

$3 \sqrt{\frac{10 (16)}{1350 x}}$

Step 2.2

Factor $10$ out of $1350 x$ .

$3 \sqrt{\frac{10 (16)}{10 (135 x)}}$

Step 2.3

Cancel the common factor.

$3 \sqrt{\frac{10 \cdot 16}{10 (135 x)}}$

Step 2.4

Rewrite the expression.

$3 \sqrt{\frac{16}{135 x}}$

Step 3

Rewrite $\frac{16}{135 x}$ as ${(\frac{4}{3})}^{2} \frac{1}{15 x}$ .

Tap for more steps...

Step 3.1

Factor the perfect power $4^{2}$ out of $16$ .

$3 \sqrt{\frac{4^{2} \cdot 1}{135 x}}$

Step 3.2

Factor the perfect power $3^{2}$ out of $135 x$ .

$3 \sqrt{\frac{4^{2} \cdot 1}{3^{2} \cdot (15 x)}}$

Step 3.3

Rearrange the fraction $\frac{4^{2} \cdot 1}{3^{2} \cdot (15 x)}$ .

$3 \sqrt{{(\frac{4}{3})}^{2} \frac{1}{15 x}}$

Step 4

Pull terms out from under the radical.

$3 (\frac{4}{3} \sqrt{\frac{1}{15 x}})$

Step 5

Rewrite $\sqrt{\frac{1}{15 x}}$ as $\frac{\sqrt{1}}{\sqrt{15 x}}$ .

$3 (\frac{4}{3} \cdot \frac{\sqrt{1}}{\sqrt{15 x}})$

Step 6

Any root of $1$ is $1$ .

$3 (\frac{4}{3} \cdot \frac{1}{\sqrt{15 x}})$

Step 7

Multiply $\frac{1}{\sqrt{15 x}}$ by $\frac{\sqrt{15 x}}{\sqrt{15 x}}$ .

$3 (\frac{4}{3} (\frac{1}{\sqrt{15 x}} \cdot \frac{\sqrt{15 x}}{\sqrt{15 x}}))$

Step 8

Combine and simplify the denominator.

Tap for more steps...

Step 8.1

Multiply $\frac{1}{\sqrt{15 x}}$ by $\frac{\sqrt{15 x}}{\sqrt{15 x}}$ .

$3 (\frac{4}{3} \cdot \frac{\sqrt{15 x}}{\sqrt{15 x} \sqrt{15 x}})$

Step 8.2

Raise $\sqrt{15 x}$ to the power of $1$ .

$3 (\frac{4}{3} \cdot \frac{\sqrt{15 x}}{{\sqrt{15 x}}^{1} \sqrt{15 x}})$

Step 8.3

Raise $\sqrt{15 x}$ to the power of $1$ .

$3 (\frac{4}{3} \cdot \frac{\sqrt{15 x}}{{\sqrt{15 x}}^{1} {\sqrt{15 x}}^{1}})$

Step 8.4

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

$3 (\frac{4}{3} \cdot \frac{\sqrt{15 x}}{{\sqrt{15 x}}^{1 + 1}})$

Step 8.5

Add $1$ and $1$ .

$3 (\frac{4}{3} \cdot \frac{\sqrt{15 x}}{{\sqrt{15 x}}^{2}})$

Step 8.6

Rewrite ${\sqrt{15 x}}^{2}$ as $15 x$ .

Tap for more steps...

Step 8.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{15 x}$ as ${(15 x)}^{\frac{1}{2}}$ .

$3 (\frac{4}{3} \cdot \frac{\sqrt{15 x}}{{({(15 x)}^{\frac{1}{2}})}^{2}})$

Step 8.6.2

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

$3 (\frac{4}{3} \cdot \frac{\sqrt{15 x}}{{(15 x)}^{\frac{1}{2} \cdot 2}})$

Step 8.6.3

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

$3 (\frac{4}{3} \cdot \frac{\sqrt{15 x}}{{(15 x)}^{\frac{2}{2}}})$

Step 8.6.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 8.6.4.1

Cancel the common factor.

$3 (\frac{4}{3} \cdot \frac{\sqrt{15 x}}{{(15 x)}^{\frac{2}{2}}})$

Step 8.6.4.2

Rewrite the expression.

$3 (\frac{4}{3} \cdot \frac{\sqrt{15 x}}{{(15 x)}^{1}})$

Step 8.6.5

Simplify.

$3 (\frac{4}{3} \cdot \frac{\sqrt{15 x}}{15 x})$

Step 9

Multiply $\frac{4}{3} \cdot \frac{\sqrt{15 x}}{15 x}$ .

Tap for more steps...

Step 9.1

Multiply $\frac{4}{3}$ by $\frac{\sqrt{15 x}}{15 x}$ .

$3 \frac{4 \sqrt{15 x}}{3 (15 x)}$

Step 9.2

Multiply $15$ by $3$ .

$3 \frac{4 \sqrt{15 x}}{45 x}$

Step 10

Cancel the common factor of $3$ .

Tap for more steps...

Step 10.1

Factor $3$ out of $45 x$ .

$3 \frac{4 \sqrt{15 x}}{3 (15 x)}$

Step 10.2

Cancel the common factor.

$3 \frac{4 \sqrt{15 x}}{3 (15 x)}$

Step 10.3

Rewrite the expression.

$\frac{4 \sqrt{15 x}}{15 x}$