Trigonometry Examples

${(\sqrt{54})}^{5}$

Step 1

Rewrite $54$ as $3^{2} \cdot 6$ .

Tap for more steps...

Step 1.1

Factor $9$ out of $54$ .

${\sqrt{9 (6)}}^{5}$

Step 1.2

Rewrite $9$ as $3^{2}$ .

${\sqrt{3^{2} \cdot 6}}^{5}$

${\sqrt{3^{2} \cdot 6}}^{5}$

Step 2

Pull terms out from under the radical.

${(3 \sqrt{6})}^{5}$

Step 3

Simplify the expression.

Tap for more steps...

Step 3.1

Apply the product rule to $3 \sqrt{6}$ .

$3^{5} {\sqrt{6}}^{5}$

Step 3.2

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

$243 {\sqrt{6}}^{5}$

$243 {\sqrt{6}}^{5}$

Step 4

Rewrite ${\sqrt{6}}^{5}$ as $\sqrt{6^{5}}$ .

$243 \sqrt{6^{5}}$

Step 5

Raise $6$ to the power of $5$ .

$243 \sqrt{7776}$

Step 6

Rewrite $7776$ as $36^{2} \cdot 6$ .

Tap for more steps...

Step 6.1

Factor $1296$ out of $7776$ .

$243 \sqrt{1296 (6)}$

Step 6.2

Rewrite $1296$ as $36^{2}$ .

$243 \sqrt{36^{2} \cdot 6}$

$243 \sqrt{36^{2} \cdot 6}$

Step 7

Pull terms out from under the radical.

$243 (36 \sqrt{6})$

Step 8

Multiply $36$ by $243$ .

$8748 \sqrt{6}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$8748 \sqrt{6}$

Decimal Form:

$21428.13626986 \dots$

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