Algebra Examples

$x^{2} \sqrt{75} - \sqrt{12 x^{4}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $75$ as $5^{2} \cdot 3$ .

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Step 1.1.1

Factor $25$ out of $75$ .

$x^{2} \sqrt{25 (3)} - \sqrt{12 x^{4}}$

Step 1.1.2

Rewrite $25$ as $5^{2}$ .

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

Step 1.2

Pull terms out from under the radical.

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

Step 1.3

The absolute value is the distance between a number and zero. The distance between $0$ and $5$ is $5$ .

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

Step 1.4

Move $5$ to the left of $x^{2}$ .

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

Step 1.5

Rewrite $12 x^{4}$ as ${(2 x^{2})}^{2} \cdot 3$ .

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Step 1.5.1

Factor $4$ out of $12$ .

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

Step 1.5.2

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

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

Step 1.5.3

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

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

Step 1.5.4

Move $3$ .

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

Step 1.5.5

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

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

Step 1.6

Pull terms out from under the radical.

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

Step 1.7

Remove non-negative terms from the absolute value.

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

Step 1.8

Multiply $2$ by $- 1$ .

$5 x^{2} \sqrt{3} - 2 x^{2} \sqrt{3}$

Step 2

Subtract $2 x^{2} \sqrt{3}$ from $5 x^{2} \sqrt{3}$ .

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