Trigonometry Examples

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

Step 1

Write $1$ as a fraction with a common denominator.

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

Step 2

Combine the numerators over the common denominator.

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

Step 3

Subtract $3$ from $5$ .

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

Step 4

Rewrite $\sqrt{\frac{2}{5}}$ as $\frac{\sqrt{2}}{\sqrt{5}}$ .

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

Step 5

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

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

Step 6

Combine and simplify the denominator.

Tap for more steps...

Step 6.1

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

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

Step 6.2

Raise $\sqrt{5}$ to the power of $1$ .

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

Step 6.3

Raise $\sqrt{5}$ to the power of $1$ .

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

Step 6.4

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

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

Step 6.5

Add $1$ and $1$ .

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

Step 6.6

Rewrite ${\sqrt{5}}^{2}$ as $5$ .

Tap for more steps...

Step 6.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

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

Step 6.6.2

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

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

Step 6.6.3

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

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

Step 6.6.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 6.6.4.1

Cancel the common factor.

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

Step 6.6.4.2

Rewrite the expression.

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

Step 6.6.5

Evaluate the exponent.

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

Step 7

Simplify the numerator.

Tap for more steps...

Step 7.1

Combine using the product rule for radicals.

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

Step 7.2

Multiply $2$ by $5$ .

$- \frac{\sqrt{10}}{5} \cdot 2$

Step 8

Multiply $- \frac{\sqrt{10}}{5} \cdot 2$ .

Tap for more steps...

Step 8.1

Multiply $2$ by $- 1$ .

$- 2 \frac{\sqrt{10}}{5}$

Step 8.2

Combine $- 2$ and $\frac{\sqrt{10}}{5}$ .

$\frac{- 2 \sqrt{10}}{5}$

Step 9

Move the negative in front of the fraction.

$- \frac{2 \sqrt{10}}{5}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$- \frac{2 \sqrt{10}}{5}$

Decimal Form:

$- 1.26491106 \dots$