Trigonometry Examples

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

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

Step 1

Multiply

- 1

$- 1$ by

- 1

$- 1$ by adding the exponents.

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Step 1.1

Move

- 1

$- 1$ .

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

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

Step 1.2

Multiply

- 1

$- 1$ by

- 1

$- 1$ .

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

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

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

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

Step 2

Multiply

{(- 1)}^{2}

${(- 1)}^{2}$ by

{(- 1)}^{2}

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

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Step 2.1

Move

{(- 1)}^{2}

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

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

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

Step 2.2

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

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

Step 2.3

Add

2

$2$ and

2

$2$ .

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

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

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

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

Step 3

Raise

\sqrt{13}

$\sqrt{13}$ to the power of

1

$1$ .

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

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

Step 4

Raise

\sqrt{13}

$\sqrt{13}$ to the power of

1

$1$ .

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

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

Step 5

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

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

Step 6

Simplify the expression.

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Step 6.1

Add

1

$1$ and

1

$1$ .

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

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

Step 6.2

Raise

- 1

$- 1$ to the power of

4

$4$ .

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

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

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

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

Step 7

Rewrite

{\sqrt{13}}^{2}

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

13

$13$ .

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Step 7.1

Use

\sqrt[n]{a^{x}} = a^{\frac{x}{n}}

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

\sqrt{13}

$\sqrt{13}$ as

13^{\frac{1}{2}}

$13^{\frac{1}{2}}$ .

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

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

Step 7.2

Apply the power rule and multiply exponents,

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

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

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

Step 7.3

Combine

\frac{1}{2}

$\frac{1}{2}$ and

2

$2$ .

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

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

Step 7.4

Cancel the common factor of

2

$2$ .

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Step 7.4.1

Cancel the common factor.

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

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

Step 7.4.2

Rewrite the expression.

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

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

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

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

Step 7.5

Evaluate the exponent.

\sqrt{1 \cdot 13}

$\sqrt{1 \cdot 13}$

\sqrt{1 \cdot 13}

$\sqrt{1 \cdot 13}$

Step 8

Multiply

13

$13$ by

1

$1$ .

\sqrt{13}

$\sqrt{13}$

Step 9

The result can be shown in multiple forms.

Exact Form:

\sqrt{13}

$\sqrt{13}$

Decimal Form:

3.60555127 \dots

$3.60555127 \dots$