Trigonometry Examples

$v ({(\sqrt{37})}^{2} - 37^{2})$

Step 1

Simplify each term.

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Step 1.1

Rewrite ${\sqrt{37}}^{2}$ as $37$ .

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Step 1.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{37}$ as $37^{\frac{1}{2}}$ .

$v ({(37^{\frac{1}{2}})}^{2} - 37^{2})$

Step 1.1.2

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

$v (37^{\frac{1}{2} \cdot 2} - 37^{2})$

Step 1.1.3

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

$v (37^{\frac{2}{2}} - 37^{2})$

Step 1.1.4

Cancel the common factor of $2$ .

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Step 1.1.4.1

Cancel the common factor.

$v (37^{\frac{2}{2}} - 37^{2})$

Step 1.1.4.2

Rewrite the expression.

$v (37^{1} - 37^{2})$

Step 1.1.5

Evaluate the exponent.

$v (37 - 37^{2})$

Step 1.2

Raise $37$ to the power of $2$ .

$v (37 - 1 \cdot 1369)$

Step 1.3

Multiply $- 1$ by $1369$ .

$v (37 - 1369)$

Step 2

Simplify the expression.

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Step 2.1

Subtract $1369$ from $37$ .

$v \cdot - 1332$

Step 2.2

Move $- 1332$ to the left of $v$ .

$- 1332 v$