Algebra Examples

$\sqrt{20} - 2 \sqrt{5}$

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 $20$ .

$\sqrt{4 (5)} - 2 \sqrt{5}$

Step 1.1.2

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

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

Step 1.2

Pull terms out from under the radical.

$| 2 | \sqrt{5} - 2 \sqrt{5}$

Step 1.3

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

$2 \sqrt{5} - 2 \sqrt{5}$

Step 2

Subtract $2 \sqrt{5}$ from $2 \sqrt{5}$ .

$0$