Trigonometry Examples

v ({(\sqrt{2})}^{2} + {(- \sqrt{2})}^{2})

$v ({(\sqrt{2})}^{2} + {(- \sqrt{2})}^{2})$

Step 1

Simplify each term.

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Step 1.1

Rewrite

{\sqrt{2}}^{2}

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

2

$2$ .

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Step 1.1.1

Use

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

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

\sqrt{2}

$\sqrt{2}$ as

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

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

v ({(2^{\frac{1}{2}})}^{2} + {(- \sqrt{2})}^{2})

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

Step 1.1.2

Apply the power rule and multiply exponents,

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

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

v (2^{\frac{1}{2} \cdot 2} + {(- \sqrt{2})}^{2})

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

Step 1.1.3

Combine

\frac{1}{2}

$\frac{1}{2}$ and

2

$2$ .

v (2^{\frac{2}{2}} + {(- \sqrt{2})}^{2})

$v (2^{\frac{2}{2}} + {(- \sqrt{2})}^{2})$

Step 1.1.4

Cancel the common factor of

2

$2$ .

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Step 1.1.4.1

Cancel the common factor.

$v (2^{\frac{2}{2}} + {(- \sqrt{2})}^{2})$

Step 1.1.4.2

Rewrite the expression.

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

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

Step 1.1.5

Evaluate the exponent.

$v (2 + {(- \sqrt{2})}^{2})$

$v (2 + {(- \sqrt{2})}^{2})$

Step 1.2

Apply the product rule to

$- \sqrt{2}$ .

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

Step 1.3

Raise

$- 1$ to the power of

$2$ .

$v (2 + 1 {\sqrt{2}}^{2})$

Step 1.4

Multiply

${\sqrt{2}}^{2}$ by

$1$ .

$v (2 + {\sqrt{2}}^{2})$

Step 1.5

Rewrite

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

$2$ .

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Step 1.5.1

Use

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

$\sqrt{2}$ as

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

$v (2 + {(2^{\frac{1}{2}})}^{2})$

Step 1.5.2

Apply the power rule and multiply exponents,

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

$v (2 + 2^{\frac{1}{2} \cdot 2})$

Step 1.5.3

Combine

$\frac{1}{2}$ and

$2$ .

$v (2 + 2^{\frac{2}{2}})$

Step 1.5.4

Cancel the common factor of

$2$ .

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Step 1.5.4.1

Cancel the common factor.

$v (2 + 2^{\frac{2}{2}})$

Step 1.5.4.2

Rewrite the expression.

$v (2 + 2^{1})$

$v (2 + 2^{1})$

Step 1.5.5

Evaluate the exponent.

$v (2 + 2)$

$v (2 + 2)$

$v (2 + 2)$

Step 2

Simplify the expression.

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Step 2.1

Add

$2$ and

$2$ .

$v \cdot 4$

Step 2.2

Move

$4$ to the left of

$v$ .

$4 v$

$4 v$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$