Algebra Examples

$5 \sqrt{12} - 19 \sqrt{3}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $4$ out of $12$ .

$5 \sqrt{4 (3)} - 19 \sqrt{3}$

Step 1.1.2

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

$5 \sqrt{2^{2} \cdot 3} - 19 \sqrt{3}$

Step 1.2

Pull terms out from under the radical.

$5 (| 2 | \sqrt{3}) - 19 \sqrt{3}$

Step 1.3

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

$5 (2 \sqrt{3}) - 19 \sqrt{3}$

Step 1.4

Multiply $2$ by $5$ .

$10 \sqrt{3} - 19 \sqrt{3}$

Step 2

Subtract $19 \sqrt{3}$ from $10 \sqrt{3}$ .

$- 9 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 9 \sqrt{3}$

Decimal Form:

$- 15.58845726 \dots$