Trigonometry Examples

$3 \sqrt{50 \cdot \sqrt{32}}$

Step 1

Rewrite $32$ as $4^{2} \cdot 2$ .

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Step 1.1

Factor $16$ out of $32$ .

$3 \sqrt{50 \sqrt{16 (2)}}$

Step 1.2

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

$3 \sqrt{50 \sqrt{4^{2} \cdot 2}}$

$3 \sqrt{50 \sqrt{4^{2} \cdot 2}}$

Step 2

Pull terms out from under the radical.

$3 \sqrt{50 \cdot 4 \sqrt{2}}$

Step 3

Multiply $50$ by $4$ .

$3 \sqrt{200 \sqrt{2}}$

Step 4

Rewrite $200 \sqrt{2}$ as $10^{2} \cdot (2 \sqrt{2})$ .

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Step 4.1

Factor $100$ out of $200$ .

$3 \sqrt{100 (2) \sqrt{2}}$

Step 4.2

Rewrite $100$ as $10^{2}$ .

$3 \sqrt{10^{2} \cdot 2 \sqrt{2}}$

Step 4.3

Add parentheses.

$3 \sqrt{10^{2} \cdot (2 \sqrt{2})}$

$3 \sqrt{10^{2} \cdot (2 \sqrt{2})}$

Step 5

Pull terms out from under the radical.

$3 (10 \sqrt{2 \sqrt{2}})$

Step 6

Multiply $10$ by $3$ .

$30 \sqrt{2 \sqrt{2}}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$30 \sqrt{2 \sqrt{2}}$

Decimal Form:

$50.45378491 \dots$

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