Trigonometry Examples

$10 \sqrt{12 x^{3}} \cdot (2 \sqrt{6 x^{3}})$

Step 1

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

Tap for more steps...

Step 1.1

Factor $4$ out of $12$ .

$10 \sqrt{4 (3) x^{3}} \cdot (2 \sqrt{6 x^{3}})$

Step 1.2

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

$10 \sqrt{2^{2} \cdot 3 x^{3}} \cdot (2 \sqrt{6 x^{3}})$

Step 1.3

Factor out $x^{2}$ .

$10 \sqrt{2^{2} \cdot 3 (x^{2} x)} \cdot (2 \sqrt{6 x^{3}})$

Step 1.4

Move $3$ .

$10 \sqrt{2^{2} x^{2} \cdot 3 x} \cdot (2 \sqrt{6 x^{3}})$

Step 1.5

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

$10 \sqrt{{(2 x)}^{2} \cdot 3 x} \cdot (2 \sqrt{6 x^{3}})$

Step 1.6

Add parentheses.

$10 \sqrt{{(2 x)}^{2} \cdot (3 x)} \cdot (2 \sqrt{6 x^{3}})$

Step 2

Pull terms out from under the radical.

$10 (2 x \sqrt{3 x}) \cdot (2 \sqrt{6 x^{3}})$

Step 3

Multiply $2$ by $10$ .

$20 (x \sqrt{3 x}) \cdot (2 \sqrt{6 x^{3}})$

Step 4

Rewrite $6 x^{3}$ as $x^{2} \cdot (6 x)$ .

Tap for more steps...

Step 4.1

Factor out $x^{2}$ .

$20 x \sqrt{3 x} \cdot (2 \sqrt{6 (x^{2} x)})$

Step 4.2

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

$20 x \sqrt{3 x} \cdot (2 \sqrt{x^{2} \cdot 6 x})$

Step 4.3

Add parentheses.

$20 x \sqrt{3 x} \cdot (2 \sqrt{x^{2} \cdot (6 x)})$

Step 5

Pull terms out from under the radical.

$20 x \sqrt{3 x} \cdot (2 (x \sqrt{6 x}))$

Step 6

Multiply $x$ by $x$ by adding the exponents.

Tap for more steps...

Step 6.1

Move $x$ .

$20 (x \cdot x) \sqrt{3 x} \cdot (2 (\sqrt{6 x}))$

Step 6.2

Multiply $x$ by $x$ .

$20 x^{2} \sqrt{3 x} \cdot (2 (\sqrt{6 x}))$

Step 7

Multiply $20 x^{2} \sqrt{3 x} (2 \sqrt{6 x})$ .

Tap for more steps...

Step 7.1

Multiply $2$ by $20$ .

$40 x^{2} \sqrt{3 x} \sqrt{6 x}$

Step 7.2

Combine using the product rule for radicals.

$40 x^{2} \sqrt{6 x (3 x)}$

Step 7.3

Multiply $3$ by $6$ .

$40 x^{2} \sqrt{18 x \cdot x}$

Step 7.4

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

$40 x^{2} \sqrt{18 (x^{1} x)}$

Step 7.5

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

$40 x^{2} \sqrt{18 (x^{1} x^{1})}$

Step 7.6

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

$40 x^{2} \sqrt{18 x^{1 + 1}}$

Step 7.7

Add $1$ and $1$ .

$40 x^{2} \sqrt{18 x^{2}}$

Step 8

Rewrite $18 x^{2}$ as ${(3 x)}^{2} \cdot 2$ .

Tap for more steps...

Step 8.1

Factor $9$ out of $18$ .

$40 x^{2} \sqrt{9 (2) x^{2}}$

Step 8.2

Rewrite $9$ as $3^{2}$ .

$40 x^{2} \sqrt{3^{2} \cdot 2 x^{2}}$

Step 8.3

Move $2$ .

$40 x^{2} \sqrt{3^{2} x^{2} \cdot 2}$

Step 8.4

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

$40 x^{2} \sqrt{{(3 x)}^{2} \cdot 2}$

Step 9

Pull terms out from under the radical.

$40 x^{2} (3 x \sqrt{2})$

Step 10

Multiply $x^{2}$ by $x$ by adding the exponents.

Tap for more steps...

Step 10.1

Move $x$ .

$40 (x \cdot x^{2}) (3 \sqrt{2})$

Step 10.2

Multiply $x$ by $x^{2}$ .

Tap for more steps...

Step 10.2.1

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

$40 (x^{1} x^{2}) (3 \sqrt{2})$

Step 10.2.2

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

$40 x^{1 + 2} (3 \sqrt{2})$

Step 10.3

Add $1$ and $2$ .

$40 x^{3} (3 \sqrt{2})$

Step 11

Multiply $3$ by $40$ .

$120 x^{3} \sqrt{2}$