Trigonometry Examples

$\sqrt{80 \cdot (3 \sqrt{20})}$

Step 1

Multiply $80$ by $3$ .

$\sqrt{240 \sqrt{20}}$

Step 2

Rewrite $20$ as $2^{2} \cdot 5$ .

Tap for more steps...

Step 2.1

Factor $4$ out of $20$ .

$\sqrt{240 \sqrt{4 (5)}}$

Step 2.2

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

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

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

Step 3

Pull terms out from under the radical.

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

Step 4

Multiply $240$ by $2$ .

$\sqrt{480 \sqrt{5}}$

Step 5

Rewrite $480 \sqrt{5}$ as ${(2^{2})}^{2} \cdot (30 \sqrt{5})$ .

Tap for more steps...

Step 5.1

Factor $16$ out of $480$ .

$\sqrt{16 (30) \sqrt{5}}$

Step 5.2

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

$\sqrt{4^{2} \cdot 30 \sqrt{5}}$

Step 5.3

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

$\sqrt{{(2^{2})}^{2} \cdot 30 \sqrt{5}}$

Step 5.4

Add parentheses.

$\sqrt{{(2^{2})}^{2} \cdot (30 \sqrt{5})}$

$\sqrt{{(2^{2})}^{2} \cdot (30 \sqrt{5})}$

Step 6

Pull terms out from under the radical.

$2^{2} \sqrt{30 \sqrt{5}}$

Step 7

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

$4 \sqrt{30 \sqrt{5}}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{30 \sqrt{5}}$

Decimal Form:

$32.76145035 \dots$

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