Basic Math Examples

$\frac{15 \sqrt{3}}{3 \sqrt{6}}$

Step 1

Cancel the common factor of $15$ and $3$ .

Tap for more steps...

Step 1.1

Factor $3$ out of $15 \sqrt{3}$ .

$\frac{3 (5 \sqrt{3})}{3 \sqrt{6}}$

Step 1.2

Cancel the common factors.

Tap for more steps...

Step 1.2.1

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

$\frac{3 (5 \sqrt{3})}{3 (\sqrt{6})}$

Step 1.2.2

Cancel the common factor.

$\frac{3 (5 \sqrt{3})}{3 \sqrt{6}}$

Step 1.2.3

Rewrite the expression.

$\frac{5 \sqrt{3}}{\sqrt{6}}$

Step 2

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

$5 \sqrt{\frac{3}{6}}$

Step 3

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

Tap for more steps...

Step 3.1

Factor $3$ out of $3$ .

$5 \sqrt{\frac{3 (1)}{6}}$

Step 3.2

Cancel the common factors.

Tap for more steps...

Step 3.2.1

Factor $3$ out of $6$ .

$5 \sqrt{\frac{3 \cdot 1}{3 \cdot 2}}$

Step 3.2.2

Cancel the common factor.

$5 \sqrt{\frac{3 \cdot 1}{3 \cdot 2}}$

Step 3.2.3

Rewrite the expression.

$5 \sqrt{\frac{1}{2}}$

Step 4

Rewrite $\sqrt{\frac{1}{2}}$ as $\frac{\sqrt{1}}{\sqrt{2}}$ .

$5 \frac{\sqrt{1}}{\sqrt{2}}$

Step 5

Any root of $1$ is $1$ .

$5 \frac{1}{\sqrt{2}}$

Step 6

Multiply $\frac{1}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$5 (\frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}})$

Step 7

Combine and simplify the denominator.

Tap for more steps...

Step 7.1

Multiply $\frac{1}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$5 \frac{\sqrt{2}}{\sqrt{2} \sqrt{2}}$

Step 7.2

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

$5 \frac{\sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}}$

Step 7.3

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

$5 \frac{\sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}}$

Step 7.4

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

$5 \frac{\sqrt{2}}{{\sqrt{2}}^{1 + 1}}$

Step 7.5

Add $1$ and $1$ .

$5 \frac{\sqrt{2}}{{\sqrt{2}}^{2}}$

Step 7.6

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

Tap for more steps...

Step 7.6.1

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

$5 \frac{\sqrt{2}}{{(2^{\frac{1}{2}})}^{2}}$

Step 7.6.2

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

$5 \frac{\sqrt{2}}{2^{\frac{1}{2} \cdot 2}}$

Step 7.6.3

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

$5 \frac{\sqrt{2}}{2^{\frac{2}{2}}}$

Step 7.6.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 7.6.4.1

Cancel the common factor.

$5 \frac{\sqrt{2}}{2^{\frac{2}{2}}}$

Step 7.6.4.2

Rewrite the expression.

$5 \frac{\sqrt{2}}{2^{1}}$

Step 7.6.5

Evaluate the exponent.

$5 \frac{\sqrt{2}}{2}$

Step 8

Combine $5$ and $\frac{\sqrt{2}}{2}$ .

$\frac{5 \sqrt{2}}{2}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{5 \sqrt{2}}{2}$

Decimal Form:

$3.53553390 \dots$