Trigonometry Examples

$\frac{5 \sqrt{5}}{15 \sqrt{2}}$

Step 1

Cancel the common factor of $5$ and $15$ .

Tap for more steps...

Step 1.1

Factor $5$ out of $5 \sqrt{5}$ .

$\frac{5 (\sqrt{5})}{15 \sqrt{2}}$

Step 1.2

Cancel the common factors.

Tap for more steps...

Step 1.2.1

Factor $5$ out of $15 \sqrt{2}$ .

$\frac{5 (\sqrt{5})}{5 (3 \sqrt{2})}$

Step 1.2.2

Cancel the common factor.

$\frac{5 \sqrt{5}}{5 (3 \sqrt{2})}$

Step 1.2.3

Rewrite the expression.

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

Step 2

Multiply $\frac{\sqrt{5}}{3 \sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

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

Step 3

Combine and simplify the denominator.

Tap for more steps...

Step 3.1

Multiply $\frac{\sqrt{5}}{3 \sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

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

Step 3.2

Move $\sqrt{2}$ .

$\frac{\sqrt{5} \sqrt{2}}{3 (\sqrt{2} \sqrt{2})}$

Step 3.3

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

$\frac{\sqrt{5} \sqrt{2}}{3 ({\sqrt{2}}^{1} \sqrt{2})}$

Step 3.4

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

$\frac{\sqrt{5} \sqrt{2}}{3 ({\sqrt{2}}^{1} {\sqrt{2}}^{1})}$

Step 3.5

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

$\frac{\sqrt{5} \sqrt{2}}{3 {\sqrt{2}}^{1 + 1}}$

Step 3.6

Add $1$ and $1$ .

$\frac{\sqrt{5} \sqrt{2}}{3 {\sqrt{2}}^{2}}$

Step 3.7

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

Tap for more steps...

Step 3.7.1

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

$\frac{\sqrt{5} \sqrt{2}}{3 {(2^{\frac{1}{2}})}^{2}}$

Step 3.7.2

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

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

Step 3.7.3

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

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

Step 3.7.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.7.4.1

Cancel the common factor.

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

Step 3.7.4.2

Rewrite the expression.

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

Step 3.7.5

Evaluate the exponent.

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

Step 4

Simplify the numerator.

Tap for more steps...

Step 4.1

Combine using the product rule for radicals.

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

Step 4.2

Multiply $5$ by $2$ .

$\frac{\sqrt{10}}{3 \cdot 2}$

Step 5

Multiply $3$ by $2$ .

$\frac{\sqrt{10}}{6}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{10}}{6}$

Decimal Form:

$0.52704627 \dots$