Trigonometry Examples

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

Step 1

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

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Step 1.1

Move $x$ .

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

Step 1.2

Reorder $6$ and $y^{2}$ .

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

Step 1.3

Add parentheses.

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

Multiply $4 \sqrt{2 x} (5 y \sqrt{6 x})$ .

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Step 3.1

Multiply $5$ by $4$ .

$20 \sqrt{2 x} (y \sqrt{6 x})$

Step 3.2

Combine using the product rule for radicals.

$20 (y \sqrt{2 x (6 x)})$

Step 3.3

Multiply $6$ by $2$ .

$20 (y \sqrt{12 x \cdot x})$

Step 3.4

Raise $x$ to the power of $1$ .

$20 (y \sqrt{12 (x^{1} x)})$

Step 3.5

Raise $x$ to the power of $1$ .

$20 (y \sqrt{12 (x^{1} x^{1})})$

Step 3.6

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$20 (y \sqrt{12 x^{1 + 1}})$

Step 3.7

Add $1$ and $1$ .

$20 (y \sqrt{12 x^{2}})$

$20 (y \sqrt{12 x^{2}})$

Step 4

Rewrite $12 x^{2}$ as ${(2 x)}^{2} \cdot 3$ .

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Step 4.1

Factor $4$ out of $12$ .

$20 (y \sqrt{4 (3) x^{2}})$

Step 4.2

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

$20 (y \sqrt{2^{2} \cdot 3 x^{2}})$

Step 4.3

Move $3$ .

$20 (y \sqrt{2^{2} x^{2} \cdot 3})$

Step 4.4

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

$20 (y \sqrt{{(2 x)}^{2} \cdot 3})$

$20 (y \sqrt{{(2 x)}^{2} \cdot 3})$

Step 5

Pull terms out from under the radical.

$20 (y (2 x \sqrt{3}))$

Step 6

Simplify the expression.

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Step 6.1

Rewrite using the commutative property of multiplication.

$20 (2 \sqrt{3} y x)$

Step 6.2

Multiply $2$ by $20$ .

$40 \sqrt{3} y x$

$40 \sqrt{3} y x$

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