Trigonometry Examples

$\sqrt{5} (2 \sqrt{5} - \sqrt{11})$

Step 1

Apply the distributive property.

$\sqrt{5} (2 \sqrt{5}) + \sqrt{5} (- \sqrt{11})$

Step 2

Multiply $\sqrt{5} (2 \sqrt{5})$ .

Tap for more steps...

Step 2.1

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

$2 ({\sqrt{5}}^{1} \sqrt{5}) + \sqrt{5} (- \sqrt{11})$

Step 2.2

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

$2 ({\sqrt{5}}^{1} {\sqrt{5}}^{1}) + \sqrt{5} (- \sqrt{11})$

Step 2.3

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

$2 {\sqrt{5}}^{1 + 1} + \sqrt{5} (- \sqrt{11})$

Step 2.4

Add $1$ and $1$ .

$2 {\sqrt{5}}^{2} + \sqrt{5} (- \sqrt{11})$

Step 3

Multiply $\sqrt{5} (- \sqrt{11})$ .

Tap for more steps...

Step 3.1

Combine using the product rule for radicals.

$2 {\sqrt{5}}^{2} - \sqrt{5 \cdot 11}$

Step 3.2

Multiply $5$ by $11$ .

$2 {\sqrt{5}}^{2} - \sqrt{55}$

Step 4

Simplify each term.

Tap for more steps...

Step 4.1

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

Tap for more steps...

Step 4.1.1

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

$2 {(5^{\frac{1}{2}})}^{2} - \sqrt{55}$

Step 4.1.2

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

$2 \cdot 5^{\frac{1}{2} \cdot 2} - \sqrt{55}$

Step 4.1.3

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

$2 \cdot 5^{\frac{2}{2}} - \sqrt{55}$

Step 4.1.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.1.4.1

Cancel the common factor.

$2 \cdot 5^{\frac{2}{2}} - \sqrt{55}$

Step 4.1.4.2

Rewrite the expression.

$2 \cdot 5^{1} - \sqrt{55}$

Step 4.1.5

Evaluate the exponent.

$2 \cdot 5 - \sqrt{55}$

Step 4.2

Multiply $2$ by $5$ .

$10 - \sqrt{55}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$10 - \sqrt{55}$

Decimal Form:

$2.58380151 \dots$