Trigonometry Examples

$2 (\frac{\sqrt{48}}{7^{2}} - 1)$

Step 1

Simplify each term.

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Step 1.1

Simplify the numerator.

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Step 1.1.1

Rewrite $48$ as $4^{2} \cdot 3$ .

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Step 1.1.1.1

Factor $16$ out of $48$ .

$2 (\frac{\sqrt{16 (3)}}{7^{2}} - 1)$

Step 1.1.1.2

Rewrite $16$ as $4^{2}$ .

$2 (\frac{\sqrt{4^{2} \cdot 3}}{7^{2}} - 1)$

Step 1.1.2

Pull terms out from under the radical.

$2 (\frac{4 \sqrt{3}}{7^{2}} - 1)$

Step 1.2

Raise $7$ to the power of $2$ .

$2 (\frac{4 \sqrt{3}}{49} - 1)$

Step 2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{49}{49}$ .

$2 (\frac{4 \sqrt{3}}{49} - 1 \cdot \frac{49}{49})$

Step 3

Combine $- 1$ and $\frac{49}{49}$ .

$2 (\frac{4 \sqrt{3}}{49} + \frac{- 1 \cdot 49}{49})$

Step 4

Simplify the expression.

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Step 4.1

Combine the numerators over the common denominator.

$2 \frac{4 \sqrt{3} - 1 \cdot 49}{49}$

Step 4.2

Multiply $- 1$ by $49$ .

$2 \frac{4 \sqrt{3} - 49}{49}$

Step 5

Combine $2$ and $\frac{4 \sqrt{3} - 49}{49}$ .

$\frac{2 (4 \sqrt{3} - 49)}{49}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{2 (4 \sqrt{3} - 49)}{49}$

Decimal Form:

$- 1.71721619 \dots$