Trigonometry Examples

$4 \sqrt{80 \cdot (3 \sqrt{50})}$

Step 1

Multiply $80$ by $3$ .

$4 \sqrt{240 \sqrt{50}}$

Step 2

Rewrite $50$ as $5^{2} \cdot 2$ .

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Step 2.1

Factor $25$ out of $50$ .

$4 \sqrt{240 \sqrt{25 (2)}}$

Step 2.2

Rewrite $25$ as $5^{2}$ .

$4 \sqrt{240 \sqrt{5^{2} \cdot 2}}$

$4 \sqrt{240 \sqrt{5^{2} \cdot 2}}$

Step 3

Pull terms out from under the radical.

$4 \sqrt{240 \cdot 5 \sqrt{2}}$

Step 4

Multiply $240$ by $5$ .

$4 \sqrt{1200 \sqrt{2}}$

Step 5

Rewrite $1200 \sqrt{2}$ as $20^{2} \cdot (3 \sqrt{2})$ .

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Step 5.1

Factor $400$ out of $1200$ .

$4 \sqrt{400 (3) \sqrt{2}}$

Step 5.2

Rewrite $400$ as $20^{2}$ .

$4 \sqrt{20^{2} \cdot 3 \sqrt{2}}$

Step 5.3

Add parentheses.

$4 \sqrt{20^{2} \cdot (3 \sqrt{2})}$

$4 \sqrt{20^{2} \cdot (3 \sqrt{2})}$

Step 6

Pull terms out from under the radical.

$4 (20 \sqrt{3 \sqrt{2}})$

Step 7

Multiply $20$ by $4$ .

$80 \sqrt{3 \sqrt{2}}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$80 \sqrt{3 \sqrt{2}}$

Decimal Form:

$164.78137151 \dots$

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