Algebra Examples

$\frac{\sqrt{6 x^{3}}}{\sqrt{3 x}} \cdot \sqrt{8 x^{2}}$

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

Rewrite $6 x^{3}$ as $x^{2} \cdot (6 x)$ .

Tap for more steps...

Step 1.1.1

Factor out $x^{2}$ .

$\frac{\sqrt{6 (x^{2} x)}}{\sqrt{3 x}} \cdot \sqrt{8 x^{2}}$

Step 1.1.2

Reorder $6$ and $x^{2}$ .

$\frac{\sqrt{x^{2} \cdot 6 x}}{\sqrt{3 x}} \cdot \sqrt{8 x^{2}}$

Step 1.1.3

Add parentheses.

$\frac{\sqrt{x^{2} \cdot (6 x)}}{\sqrt{3 x}} \cdot \sqrt{8 x^{2}}$

Step 1.2

Pull terms out from under the radical.

$\frac{x \sqrt{6 x}}{\sqrt{3 x}} \cdot \sqrt{8 x^{2}}$

Step 2

Combine $\sqrt{6 x}$ and $\sqrt{3 x}$ into a single radical.

$x \sqrt{\frac{6 x}{3 x}} \cdot \sqrt{8 x^{2}}$

Step 3

Reduce the expression $\frac{6 x}{3 x}$ by cancelling the common factors.

Tap for more steps...

Step 3.1

Factor $3$ out of $6 x$ .

$x \sqrt{\frac{3 (2 x)}{3 x}} \cdot \sqrt{8 x^{2}}$

Step 3.2

Factor $3$ out of $3 x$ .

$x \sqrt{\frac{3 (2 x)}{3 (x)}} \cdot \sqrt{8 x^{2}}$

Step 3.3

Cancel the common factor.

$x \sqrt{\frac{3 (2 x)}{3 x}} \cdot \sqrt{8 x^{2}}$

Step 3.4

Rewrite the expression.

$x \sqrt{\frac{2 x}{x}} \cdot \sqrt{8 x^{2}}$

Step 4

Cancel the common factor of $x$ .

Tap for more steps...

Step 4.1

Cancel the common factor.

$x \sqrt{\frac{2 x}{x}} \cdot \sqrt{8 x^{2}}$

Step 4.2

Divide $2$ by $1$ .

$x \sqrt{2} \cdot \sqrt{8 x^{2}}$

Step 5

Rewrite $8 x^{2}$ as ${(2 x)}^{2} \cdot 2$ .

Tap for more steps...

Step 5.1

Factor $4$ out of $8$ .

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

Step 5.2

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

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

Step 5.3

Move $2$ .

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

Step 5.4

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

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

Step 6

Pull terms out from under the radical.

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

Step 7

Multiply $x$ by $x$ by adding the exponents.

Tap for more steps...

Step 7.1

Move $x$ .

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

Step 7.2

Multiply $x$ by $x$ .

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

Step 8

Multiply $x^{2} \sqrt{2} (2 \sqrt{2})$ .

Tap for more steps...

Step 8.1

Raise $\sqrt{2}$ to the power of $1$ .

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

Step 8.2

Raise $\sqrt{2}$ to the power of $1$ .

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

Step 8.3

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

$x^{2} (2 {\sqrt{2}}^{1 + 1})$

Step 8.4

Add $1$ and $1$ .

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

Step 9

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

Tap for more steps...

Step 9.1

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

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

Step 9.2

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

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

Step 9.3

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

$x^{2} (2 \cdot 2^{\frac{2}{2}})$

Step 9.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 9.4.1

Cancel the common factor.

$x^{2} (2 \cdot 2^{\frac{2}{2}})$

Step 9.4.2

Rewrite the expression.

$x^{2} (2 \cdot 2^{1})$

Step 9.5

Evaluate the exponent.

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

Step 10

Simplify the expression.

Tap for more steps...

Step 10.1

Multiply $2$ by $2$ .

$x^{2} \cdot 4$

Step 10.2

Move $4$ to the left of $x^{2}$ .

$4 x^{2}$