Calculus Examples

$\frac{1}{\sqrt{12}} \cdot (4.2 - 2)$

Step 1

Simplify the denominator.

Tap for more steps...

Step 1.1

Rewrite $12$ as $2^{2} \cdot 3$ .

Tap for more steps...

Step 1.1.1

Factor $4$ out of $12$ .

$\frac{1}{\sqrt{4 (3)}} \cdot (4.2 - 2)$

Step 1.1.2

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

$\frac{1}{\sqrt{2^{2} \cdot 3}} \cdot (4.2 - 2)$

Step 1.2

Pull terms out from under the radical.

$\frac{1}{2 \sqrt{3}} \cdot (4.2 - 2)$

Step 2

Multiply $\frac{1}{2 \sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$\frac{1}{2 \sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} \cdot (4.2 - 2)$

Step 3

Combine and simplify the denominator.

Tap for more steps...

Step 3.1

Multiply $\frac{1}{2 \sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$\frac{\sqrt{3}}{2 \sqrt{3} \sqrt{3}} \cdot (4.2 - 2)$

Step 3.2

Move $\sqrt{3}$ .

$\frac{\sqrt{3}}{2 (\sqrt{3} \sqrt{3})} \cdot (4.2 - 2)$

Step 3.3

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

$\frac{\sqrt{3}}{2 ({\sqrt{3}}^{1} \sqrt{3})} \cdot (4.2 - 2)$

Step 3.4

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

$\frac{\sqrt{3}}{2 ({\sqrt{3}}^{1} {\sqrt{3}}^{1})} \cdot (4.2 - 2)$

Step 3.5

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

$\frac{\sqrt{3}}{2 {\sqrt{3}}^{1 + 1}} \cdot (4.2 - 2)$

Step 3.6

Add $1$ and $1$ .

$\frac{\sqrt{3}}{2 {\sqrt{3}}^{2}} \cdot (4.2 - 2)$

Step 3.7

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

Tap for more steps...

Step 3.7.1

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

$\frac{\sqrt{3}}{2 {(3^{\frac{1}{2}})}^{2}} \cdot (4.2 - 2)$

Step 3.7.2

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

$\frac{\sqrt{3}}{2 \cdot 3^{\frac{1}{2} \cdot 2}} \cdot (4.2 - 2)$

Step 3.7.3

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

$\frac{\sqrt{3}}{2 \cdot 3^{\frac{2}{2}}} \cdot (4.2 - 2)$

Step 3.7.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.7.4.1

Cancel the common factor.

$\frac{\sqrt{3}}{2 \cdot 3^{\frac{2}{2}}} \cdot (4.2 - 2)$

Step 3.7.4.2

Rewrite the expression.

$\frac{\sqrt{3}}{2 \cdot 3^{1}} \cdot (4.2 - 2)$

Step 3.7.5

Evaluate the exponent.

$\frac{\sqrt{3}}{2 \cdot 3} \cdot (4.2 - 2)$

Step 4

Simplify the expression.

Tap for more steps...

Step 4.1

Multiply $2$ by $3$ .

$\frac{\sqrt{3}}{6} \cdot (4.2 - 2)$

Step 4.2

Subtract $2$ from $4.2$ .

$\frac{\sqrt{3}}{6} \cdot 2.2$

Step 5

Multiply $\frac{\sqrt{3}}{6} \cdot 2.2$ .

Tap for more steps...

Step 5.1

Combine $\frac{\sqrt{3}}{6}$ and $2.2$ .

$\frac{\sqrt{3} \cdot 2.2}{6}$

Step 5.2

Multiply $\sqrt{3}$ by $2.2$ .

$\frac{3.81051177}{6}$

Step 6

Divide $3.81051177$ by $6$ .

$0.63508529$