Trigonometry Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the product rule to $- 5 \sqrt{2}$ .

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

Step 1.2

Raise $- 5$ to the power of $2$ .

$v (25 {\sqrt{2}}^{2} + 5^{2})$

Step 1.3

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

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Step 1.3.1

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

$v (25 {(2^{\frac{1}{2}})}^{2} + 5^{2})$

Step 1.3.2

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

$v (25 \cdot 2^{\frac{1}{2} \cdot 2} + 5^{2})$

Step 1.3.3

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

$v (25 \cdot 2^{\frac{2}{2}} + 5^{2})$

Step 1.3.4

Cancel the common factor of $2$ .

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Step 1.3.4.1

Cancel the common factor.

$v (25 \cdot 2^{\frac{2}{2}} + 5^{2})$

Step 1.3.4.2

Rewrite the expression.

$v (25 \cdot 2^{1} + 5^{2})$

Step 1.3.5

Evaluate the exponent.

$v (25 \cdot 2 + 5^{2})$

Step 1.4

Multiply $25$ by $2$ .

$v (50 + 5^{2})$

Step 1.5

Raise $5$ to the power of $2$ .

$v (50 + 25)$

Step 2

Simplify the expression.

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Step 2.1

Add $50$ and $25$ .

$v \cdot 75$

Step 2.2

Move $75$ to the left of $v$ .

$75 v$