Trigonometry Examples

${(3 \sqrt{2})}^{5}$

Step 1

Apply the product rule to $3 \sqrt{2}$ .

$3^{5} {\sqrt{2}}^{5}$

Step 2

Raise $3$ to the power of $5$ .

$243 {\sqrt{2}}^{5}$

Step 3

Rewrite ${\sqrt{2}}^{5}$ as $\sqrt{2^{5}}$ .

$243 \sqrt{2^{5}}$

Step 4

Raise $2$ to the power of $5$ .

$243 \sqrt{32}$

Step 5

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

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Step 5.1

Factor $16$ out of $32$ .

$243 \sqrt{16 (2)}$

Step 5.2

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

$243 \sqrt{4^{2} \cdot 2}$

$243 \sqrt{4^{2} \cdot 2}$

Step 6

Pull terms out from under the radical.

$243 (4 \sqrt{2})$

Step 7

Multiply $4$ by $243$ .

$972 \sqrt{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$972 \sqrt{2}$

Decimal Form:

$1374.61558262 \dots$

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