Precalculus Examples

$5 \sqrt{6 {(2 x)}^{2}}$

Step 1

Apply the product rule to $2 x$ .

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

Step 2

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

$5 \sqrt{6 \cdot 4 x^{2}}$

Step 3

Multiply $6$ by $4$ .

$5 \sqrt{24 x^{2}}$

Step 4

Rewrite $24 x^{2}$ as ${(2 x)}^{2} \cdot 6$ .

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Step 4.1

Factor $4$ out of $24$ .

$5 \sqrt{4 (6) x^{2}}$

Step 4.2

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

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

Step 4.3

Move $6$ .

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

Step 4.4

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

$5 \sqrt{{(2 x)}^{2} \cdot 6}$

$5 \sqrt{{(2 x)}^{2} \cdot 6}$

Step 5

Pull terms out from under the radical.

$5 (2 x \sqrt{6})$

Step 6

Multiply $2$ by $5$ .

$10 x \sqrt{6}$

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