Trigonometry Examples

$\sqrt{6 x^{4}} \cdot (4 \sqrt{10 x})$

Step 1

Rewrite using the commutative property of multiplication.

$4 \sqrt{6 x^{4}} \sqrt{10 x}$

Step 2

Rewrite $6 x^{4}$ as ${(x^{2})}^{2} \cdot 6$ .

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Step 2.1

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$4 \sqrt{6 {(x^{2})}^{2}} \sqrt{10 x}$

Step 2.2

Reorder $6$ and ${(x^{2})}^{2}$ .

$4 \sqrt{{(x^{2})}^{2} \cdot 6} \sqrt{10 x}$

$4 \sqrt{{(x^{2})}^{2} \cdot 6} \sqrt{10 x}$

Step 3

Pull terms out from under the radical.

$4 (x^{2} \sqrt{6}) \sqrt{10 x}$

Step 4

Multiply $4 x^{2} \sqrt{6} \sqrt{10 x}$ .

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Step 4.1

Combine using the product rule for radicals.

$4 x^{2} \sqrt{10 x \cdot 6}$

Step 4.2

Multiply $6$ by $10$ .

$4 x^{2} \sqrt{60 x}$

$4 x^{2} \sqrt{60 x}$

Step 5

Rewrite $60 x$ as $2^{2} \cdot (15 x)$ .

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Step 5.1

Factor $4$ out of $60$ .

$4 x^{2} \sqrt{4 (15) x}$

Step 5.2

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

$4 x^{2} \sqrt{2^{2} \cdot 15 x}$

Step 5.3

Add parentheses.

$4 x^{2} \sqrt{2^{2} \cdot (15 x)}$

$4 x^{2} \sqrt{2^{2} \cdot (15 x)}$

Step 6

Pull terms out from under the radical.

$4 x^{2} (2 \sqrt{15 x})$

Step 7

Multiply $2$ by $4$ .

$8 x^{2} \sqrt{15 x}$

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