Algebra Examples

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

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

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

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

$27 {\sqrt{2}}^{3}$

Rewrite ${\sqrt{2}}^{3}$ as ${(2^{3})}^{\frac{1}{2}}$ .

$27 \sqrt{2^{3}}$

Raise $2$ to the power of $3$ .

$27 \sqrt{8}$

Rewrite $8$ as $2^{2} \cdot 2$ .

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Factor $4$ out of $8$ .

$27 \sqrt{4 (2)}$

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

$27 \sqrt{2^{2} \cdot 2}$

Pull terms out from under the radical.

$27 (2 \sqrt{2})$

Multiply $2$ by $27$ .

$54 \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$54 \sqrt{2}$

Decimal Form:

$76.36753236 \dots$