Algebra Examples

$- 3 \sqrt{20} - \sqrt{5}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $20$ as $2^{2} \cdot 5$ .

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Step 1.1.1

Factor $4$ out of $20$ .

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

Step 1.1.2

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

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

Step 1.2

Pull terms out from under the radical.

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

Step 1.3

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

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

Step 1.4

Multiply $2$ by $- 3$ .

$- 6 \sqrt{5} - \sqrt{5}$

Step 2

Subtract $\sqrt{5}$ from $- 6 \sqrt{5}$ .

$- 7 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 7 \sqrt{5}$

Decimal Form:

$- 15.65247584 \dots$