Trigonometry Examples

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

Step 1

Simplify each term.

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Step 1.1

One to any power is one.

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

Step 1.2

Raise $- 2$ to the power of $2$ .

$v (1 + 4 + {(4 \sqrt{2})}^{2})$

Step 1.3

Apply the product rule to $4 \sqrt{2}$ .

$v (1 + 4 + 4^{2} {\sqrt{2}}^{2})$

Step 1.4

Raise $4$ to the power of $2$ .

$v (1 + 4 + 16 {\sqrt{2}}^{2})$

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

$v (1 + 4 + 16 {(2^{\frac{1}{2}})}^{2})$

Step 1.5.2

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

$v (1 + 4 + 16 \cdot 2^{\frac{1}{2} \cdot 2})$

Step 1.5.3

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

$v (1 + 4 + 16 \cdot 2^{\frac{2}{2}})$

Step 1.5.4

Cancel the common factor of $2$ .

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Step 1.5.4.1

Cancel the common factor.

$v (1 + 4 + 16 \cdot 2^{\frac{2}{2}})$

Step 1.5.4.2

Rewrite the expression.

$v (1 + 4 + 16 \cdot 2^{1})$

Step 1.5.5

Evaluate the exponent.

$v (1 + 4 + 16 \cdot 2)$

Step 1.6

Multiply $16$ by $2$ .

$v (1 + 4 + 32)$

Step 2

Simplify the expression.

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Step 2.1

Add $1$ and $4$ .

$v (5 + 32)$

Step 2.2

Add $5$ and $32$ .

$v \cdot 37$

Step 2.3

Move $37$ to the left of $v$ .

$37 v$