Basic Math Examples

$\frac{1}{2}$ , $\frac{1}{4} \cdot \frac{1}{6}$

Step 1

Multiply $\frac{1}{4} \cdot \frac{1}{6}$ .

Tap for more steps...

Step 1.1

Multiply $\frac{1}{4}$ by $\frac{1}{6}$ .

$\frac{1}{2}, \frac{1}{4 \cdot 6}$

Step 1.2

Multiply $4$ by $6$ .

$\frac{1}{2}, \frac{1}{24}$

Step 2

Use the formula to find the geometric mean.

$\sqrt{\frac{1}{2} \cdot \frac{1}{24}}$

Step 3

Multiply $\frac{1}{2}$ by $\frac{1}{24}$ .

$\sqrt{\frac{1}{2 \cdot 24}}$

Step 4

Multiply $2$ by $24$ .

$\sqrt{\frac{1}{48}}$

Step 5

Rewrite $\sqrt{\frac{1}{48}}$ as $\frac{\sqrt{1}}{\sqrt{48}}$ .

$\frac{\sqrt{1}}{\sqrt{48}}$

Step 6

Any root of $1$ is $1$ .

$\frac{1}{\sqrt{48}}$

Step 7

Simplify the denominator.

Tap for more steps...

Step 7.1

Rewrite $48$ as $4^{2} \cdot 3$ .

Tap for more steps...

Step 7.1.1

Factor $16$ out of $48$ .

$\frac{1}{\sqrt{16 (3)}}$

Step 7.1.2

Rewrite $16$ as $4^{2}$ .

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

Step 7.2

Pull terms out from under the radical.

$\frac{1}{4 \sqrt{3}}$

Step 8

Multiply $\frac{1}{4 \sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$\frac{1}{4 \sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}$

Step 9

Combine and simplify the denominator.

Tap for more steps...

Step 9.1

Multiply $\frac{1}{4 \sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$\frac{\sqrt{3}}{4 \sqrt{3} \sqrt{3}}$

Step 9.2

Move $\sqrt{3}$ .

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

Step 9.3

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

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

Step 9.4

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

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

Step 9.5

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

$\frac{\sqrt{3}}{4 {\sqrt{3}}^{1 + 1}}$

Step 9.6

Add $1$ and $1$ .

$\frac{\sqrt{3}}{4 {\sqrt{3}}^{2}}$

Step 9.7

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

Tap for more steps...

Step 9.7.1

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

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

Step 9.7.2

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

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

Step 9.7.3

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

$\frac{\sqrt{3}}{4 \cdot 3^{\frac{2}{2}}}$

Step 9.7.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 9.7.4.1

Cancel the common factor.

$\frac{\sqrt{3}}{4 \cdot 3^{\frac{2}{2}}}$

Step 9.7.4.2

Rewrite the expression.

$\frac{\sqrt{3}}{4 \cdot 3^{1}}$

Step 9.7.5

Evaluate the exponent.

$\frac{\sqrt{3}}{4 \cdot 3}$

Step 10

Multiply $4$ by $3$ .

$\frac{\sqrt{3}}{12}$

Step 11

Approximate the result.

$0.14433756$

Step 12

The geometric mean should be rounded to one more decimal place than the original data. If the original data were mixed, round to one decimal place more than the least precise.

$0.1$