Pre-Algebra Examples

$3 {(\sqrt{32 x})}^{3}$

Step 1

Rewrite $32 x$ as ${(2^{2})}^{2} \cdot (2 x)$ .

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Step 1.1

Factor $16$ out of $32$ .

$3 {\sqrt{16 (2) x}}^{3}$

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

Add parentheses.

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

Simplify the expression.

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Step 3.1

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

$3 {(4 \sqrt{2 x})}^{3}$

Step 3.2

Apply the product rule to $4 \sqrt{2 x}$ .

$3 (4^{3} {\sqrt{2 x}}^{3})$

Step 3.3

Raise $4$ to the power of $3$ .

$3 (64 {\sqrt{2 x}}^{3})$

$3 (64 {\sqrt{2 x}}^{3})$

Step 4

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

$3 (64 \sqrt{{(2 x)}^{3}})$

Step 5

Apply the product rule to $2 x$ .

$3 (64 \sqrt{2^{3} x^{3}})$

Step 6

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

$3 (64 \sqrt{8 x^{3}})$

Step 7

Rewrite $8 x^{3}$ as ${(2 x)}^{2} \cdot (2 x)$ .

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Step 7.1

Factor $4$ out of $8$ .

$3 (64 \sqrt{4 (2) x^{3}})$

Step 7.2

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

$3 (64 \sqrt{2^{2} \cdot 2 x^{3}})$

Step 7.3

Factor out $x^{2}$ .

$3 (64 \sqrt{2^{2} \cdot 2 (x^{2} x)})$

Step 7.4

Move $2$ .

$3 (64 \sqrt{2^{2} x^{2} \cdot 2 x})$

Step 7.5

Rewrite $2^{2} x^{2}$ as ${(2 x)}^{2}$ .

$3 (64 \sqrt{{(2 x)}^{2} \cdot 2 x})$

Step 7.6

Add parentheses.

$3 (64 \sqrt{{(2 x)}^{2} \cdot (2 x)})$

$3 (64 \sqrt{{(2 x)}^{2} \cdot (2 x)})$

Step 8

Pull terms out from under the radical.

$3 (64 (2 x \sqrt{2 x}))$

Step 9

Multiply.

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Step 9.1

Multiply $2$ by $64$ .

$3 (128 (x \sqrt{2 x}))$

Step 9.2

Multiply $128$ by $3$ .

$384 x \sqrt{2 x}$

$384 x \sqrt{2 x}$

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