Trigonometry Examples

$\sqrt{(- \sqrt{13}) (- \sqrt{13}) {(- 1)}^{2}}$

Step 1

Multiply $- 1$ by $- 1$ by adding the exponents.

Tap for more steps...

Step 1.1

Move $- 1$ .

$\sqrt{- - 1 \sqrt{13} \sqrt{13} {(- 1)}^{2}}$

Step 1.2

Multiply $- 1$ by $- 1$ .

$\sqrt{{(- 1)}^{2} \sqrt{13} \sqrt{13} {(- 1)}^{2}}$

Step 2

Multiply ${(- 1)}^{2}$ by ${(- 1)}^{2}$ by adding the exponents.

Tap for more steps...

Step 2.1

Move ${(- 1)}^{2}$ .

$\sqrt{{(- 1)}^{2} {(- 1)}^{2} \sqrt{13} \sqrt{13}}$

Step 2.2

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

$\sqrt{{(- 1)}^{2 + 2} \sqrt{13} \sqrt{13}}$

Step 2.3

Add $2$ and $2$ .

$\sqrt{{(- 1)}^{4} \sqrt{13} \sqrt{13}}$

Step 3

Raise $\sqrt{13}$ to the power of $1$ .

$\sqrt{{(- 1)}^{4} ({\sqrt{13}}^{1} \sqrt{13})}$

Step 4

Raise $\sqrt{13}$ to the power of $1$ .

$\sqrt{{(- 1)}^{4} ({\sqrt{13}}^{1} {\sqrt{13}}^{1})}$

Step 5

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

$\sqrt{{(- 1)}^{4} {\sqrt{13}}^{1 + 1}}$

Step 6

Simplify the expression.

Tap for more steps...

Step 6.1

Add $1$ and $1$ .

$\sqrt{{(- 1)}^{4} {\sqrt{13}}^{2}}$

Step 6.2

Raise $- 1$ to the power of $4$ .

$\sqrt{1 {\sqrt{13}}^{2}}$

Step 7

Rewrite ${\sqrt{13}}^{2}$ as $13$ .

Tap for more steps...

Step 7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{13}$ as $13^{\frac{1}{2}}$ .

$\sqrt{1 {(13^{\frac{1}{2}})}^{2}}$

Step 7.2

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

$\sqrt{1 \cdot 13^{\frac{1}{2} \cdot 2}}$

Step 7.3

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

$\sqrt{1 \cdot 13^{\frac{2}{2}}}$

Step 7.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 7.4.1

Cancel the common factor.

$\sqrt{1 \cdot 13^{\frac{2}{2}}}$

Step 7.4.2

Rewrite the expression.

$\sqrt{1 \cdot 13^{1}}$

Step 7.5

Evaluate the exponent.

$\sqrt{1 \cdot 13}$

Step 8

Multiply $13$ by $1$ .

$\sqrt{13}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\sqrt{13}$

Decimal Form:

$3.60555127 \dots$