Trigonometry Examples

$\frac{8 (\sqrt{9})}{2 \sqrt{72}}$

Step 1

Cancel the common factor of $8$ and $2$ .

Tap for more steps...

Step 1.1

Factor $2$ out of $8 (\sqrt{9})$ .

$\frac{2 (4 \sqrt{9})}{2 \sqrt{72}}$

Step 1.2

Cancel the common factors.

Tap for more steps...

Step 1.2.1

Factor $2$ out of $2 \sqrt{72}$ .

$\frac{2 (4 \sqrt{9})}{2 (\sqrt{72})}$

Step 1.2.2

Cancel the common factor.

$\frac{2 (4 \sqrt{9})}{2 \sqrt{72}}$

Step 1.2.3

Rewrite the expression.

$\frac{4 \sqrt{9}}{\sqrt{72}}$

Step 2

Combine $\sqrt{9}$ and $\sqrt{72}$ into a single radical.

$4 \sqrt{\frac{9}{72}}$

Step 3

Cancel the common factor of $9$ and $72$ .

Tap for more steps...

Step 3.1

Factor $9$ out of $9$ .

$4 \sqrt{\frac{9 (1)}{72}}$

Step 3.2

Cancel the common factors.

Tap for more steps...

Step 3.2.1

Factor $9$ out of $72$ .

$4 \sqrt{\frac{9 \cdot 1}{9 \cdot 8}}$

Step 3.2.2

Cancel the common factor.

$4 \sqrt{\frac{9 \cdot 1}{9 \cdot 8}}$

Step 3.2.3

Rewrite the expression.

$4 \sqrt{\frac{1}{8}}$

Step 4

Rewrite $\sqrt{\frac{1}{8}}$ as $\frac{\sqrt{1}}{\sqrt{8}}$ .

$4 \frac{\sqrt{1}}{\sqrt{8}}$

Step 5

Any root of $1$ is $1$ .

$4 \frac{1}{\sqrt{8}}$

Step 6

Simplify the denominator.

Tap for more steps...

Step 6.1

Rewrite $8$ as $2^{2} \cdot 2$ .

Tap for more steps...

Step 6.1.1

Factor $4$ out of $8$ .

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

Step 6.1.2

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

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

Step 6.2

Pull terms out from under the radical.

$4 \frac{1}{2 \sqrt{2}}$

Step 7

Simplify terms.

Tap for more steps...

Step 7.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 7.1.1

Factor $2$ out of $4$ .

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

Step 7.1.2

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

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

Step 7.1.3

Cancel the common factor.

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

Step 7.1.4

Rewrite the expression.

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

Step 7.2

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

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

Step 8

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

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

Step 9

Combine and simplify the denominator.

Tap for more steps...

Step 9.1

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

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

Step 9.2

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

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

Step 9.3

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

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

Step 9.4

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

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

Step 9.5

Add $1$ and $1$ .

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

Step 9.6

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

Tap for more steps...

Step 9.6.1

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

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

Step 9.6.2

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

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

Step 9.6.3

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

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

Step 9.6.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 9.6.4.1

Cancel the common factor.

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

Step 9.6.4.2

Rewrite the expression.

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

Step 9.6.5

Evaluate the exponent.

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

Step 10

Cancel the common factor of $2$ .

Tap for more steps...

Step 10.1

Cancel the common factor.

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

Step 10.2

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

$\sqrt{2}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\sqrt{2}$

Decimal Form:

$1.41421356 \dots$