Trigonometry Examples

$5 x^{2} \sqrt{48 z} - \sqrt{12 z^{5}}$

Step 1

Rewrite $48 z$ as ${(2^{2})}^{2} \cdot (3 z)$ .

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Step 1.1

Factor $16$ out of $48$ .

$5 x^{2} \sqrt{16 (3) z} - \sqrt{12 z^{5}}$

Step 1.2

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

$5 x^{2} \sqrt{4^{2} \cdot 3 z} - \sqrt{12 z^{5}}$

Step 1.3

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

$5 x^{2} \sqrt{{(2^{2})}^{2} \cdot 3 z} - \sqrt{12 z^{5}}$

Step 1.4

Add parentheses.

$5 x^{2} \sqrt{{(2^{2})}^{2} \cdot (3 z)} - \sqrt{12 z^{5}}$

Step 2

Pull terms out from under the radical.

$5 x^{2} (2^{2} \sqrt{3 z}) - \sqrt{12 z^{5}}$

Step 3

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

$5 x^{2} (4 \sqrt{3 z}) - \sqrt{12 z^{5}}$

Step 4

Multiply $4$ by $5$ .

$20 x^{2} \sqrt{3 z} - \sqrt{12 z^{5}}$

Step 5

Rewrite $12 z^{5}$ as ${(2 z^{2})}^{2} \cdot (3 z)$ .

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Step 5.1

Factor $4$ out of $12$ .

$20 x^{2} \sqrt{3 z} - \sqrt{4 (3) z^{5}}$

Step 5.2

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

$20 x^{2} \sqrt{3 z} - \sqrt{2^{2} \cdot 3 z^{5}}$

Step 5.3

Factor out $z^{4}$ .

$20 x^{2} \sqrt{3 z} - \sqrt{2^{2} \cdot 3 (z^{4} z)}$

Step 5.4

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

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

Step 5.5

Move $3$ .

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

Step 5.6

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

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

Step 5.7

Add parentheses.

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

Step 6

Pull terms out from under the radical.

$20 x^{2} \sqrt{3 z} - (2 z^{2} \sqrt{3 z})$

Step 7

Multiply $2$ by $- 1$ .

$20 x^{2} \sqrt{3 z} - 2 z^{2} \sqrt{3 z}$