Algebra Examples

$\frac{18 \sqrt{2}}{3 \sqrt{3}}$

Step 1

Cancel the common factor of $18$ and $3$ .

Tap for more steps...

Step 1.1

Factor $3$ out of $18 \sqrt{2}$ .

$\frac{3 (6 \sqrt{2})}{3 \sqrt{3}}$

Step 1.2

Cancel the common factors.

Tap for more steps...

Step 1.2.1

Factor $3$ out of $3 \sqrt{3}$ .

$\frac{3 (6 \sqrt{2})}{3 (\sqrt{3})}$

Step 1.2.2

Cancel the common factor.

$\frac{3 (6 \sqrt{2})}{3 \sqrt{3}}$

Step 1.2.3

Rewrite the expression.

$\frac{6 \sqrt{2}}{\sqrt{3}}$

Step 2

Multiply $\frac{6 \sqrt{2}}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$\frac{6 \sqrt{2}}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}$

Step 3

Combine and simplify the denominator.

Tap for more steps...

Step 3.1

Multiply $\frac{6 \sqrt{2}}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$\frac{6 \sqrt{2} \sqrt{3}}{\sqrt{3} \sqrt{3}}$

Step 3.2

Raise $\sqrt{3}$ to the power of $1$ .

$\frac{6 \sqrt{2} \sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}}$

Step 3.3

Raise $\sqrt{3}$ to the power of $1$ .

$\frac{6 \sqrt{2} \sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}}$

Step 3.4

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

$\frac{6 \sqrt{2} \sqrt{3}}{{\sqrt{3}}^{1 + 1}}$

Step 3.5

Add $1$ and $1$ .

$\frac{6 \sqrt{2} \sqrt{3}}{{\sqrt{3}}^{2}}$

Step 3.6

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

Tap for more steps...

Step 3.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$\frac{6 \sqrt{2} \sqrt{3}}{{(3^{\frac{1}{2}})}^{2}}$

Step 3.6.2

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

$\frac{6 \sqrt{2} \sqrt{3}}{3^{\frac{1}{2} \cdot 2}}$

Step 3.6.3

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

$\frac{6 \sqrt{2} \sqrt{3}}{3^{\frac{2}{2}}}$

Step 3.6.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.6.4.1

Cancel the common factor.

$\frac{6 \sqrt{2} \sqrt{3}}{3^{\frac{2}{2}}}$

Step 3.6.4.2

Rewrite the expression.

$\frac{6 \sqrt{2} \sqrt{3}}{3^{1}}$

Step 3.6.5

Evaluate the exponent.

$\frac{6 \sqrt{2} \sqrt{3}}{3}$

Step 4

Cancel the common factor of $6$ and $3$ .

Tap for more steps...

Step 4.1

Factor $3$ out of $6 \sqrt{2} \sqrt{3}$ .

$\frac{3 (2 \sqrt{2} \sqrt{3})}{3}$

Step 4.2

Cancel the common factors.

Tap for more steps...

Step 4.2.1

Factor $3$ out of $3$ .

$\frac{3 (2 \sqrt{2} \sqrt{3})}{3 (1)}$

Step 4.2.2

Cancel the common factor.

$\frac{3 (2 \sqrt{2} \sqrt{3})}{3 \cdot 1}$

Step 4.2.3

Rewrite the expression.

$\frac{2 \sqrt{2} \sqrt{3}}{1}$

Step 4.2.4

Divide $2 \sqrt{2} \sqrt{3}$ by $1$ .

$2 \sqrt{2} \sqrt{3}$

Step 5

Multiply $2 \sqrt{2} \sqrt{3}$ .

Tap for more steps...

Step 5.1

Combine using the product rule for radicals.

$2 \sqrt{3 \cdot 2}$

Step 5.2

Multiply $3$ by $2$ .

$2 \sqrt{6}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{6}$

Decimal Form:

$4.89897948 \dots$