Algebra Examples

$\sqrt{20} + 2 \sqrt{80} + \sqrt{72} - \sqrt{5}$

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 $20$ .

$\sqrt{4 (5)} + 2 \sqrt{80} + \sqrt{72} - \sqrt{5}$

Step 1.1.2

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

$\sqrt{2^{2} \cdot 5} + 2 \sqrt{80} + \sqrt{72} - \sqrt{5}$

Step 1.2

Pull terms out from under the radical.

$| 2 | \sqrt{5} + 2 \sqrt{80} + \sqrt{72} - \sqrt{5}$

Step 1.3

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

$2 \sqrt{5} + 2 \sqrt{80} + \sqrt{72} - \sqrt{5}$

Step 1.4

Rewrite $80$ as $4^{2} \cdot 5$ .

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Step 1.4.1

Factor $16$ out of $80$ .

$2 \sqrt{5} + 2 \sqrt{16 (5)} + \sqrt{72} - \sqrt{5}$

Step 1.4.2

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

$2 \sqrt{5} + 2 \sqrt{4^{2} \cdot 5} + \sqrt{72} - \sqrt{5}$

Step 1.5

Pull terms out from under the radical.

$2 \sqrt{5} + 2 (| 4 | \sqrt{5}) + \sqrt{72} - \sqrt{5}$

Step 1.6

The absolute value is the distance between a number and zero. The distance between $0$ and $4$ is $4$ .

$2 \sqrt{5} + 2 (4 \sqrt{5}) + \sqrt{72} - \sqrt{5}$

Step 1.7

Multiply $4$ by $2$ .

$2 \sqrt{5} + 8 \sqrt{5} + \sqrt{72} - \sqrt{5}$

Step 1.8

Rewrite $72$ as $6^{2} \cdot 2$ .

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Step 1.8.1

Factor $36$ out of $72$ .

$2 \sqrt{5} + 8 \sqrt{5} + \sqrt{36 (2)} - \sqrt{5}$

Step 1.8.2

Rewrite $36$ as $6^{2}$ .

$2 \sqrt{5} + 8 \sqrt{5} + \sqrt{6^{2} \cdot 2} - \sqrt{5}$

Step 1.9

Pull terms out from under the radical.

$2 \sqrt{5} + 8 \sqrt{5} + | 6 | \sqrt{2} - \sqrt{5}$

Step 1.10

The absolute value is the distance between a number and zero. The distance between $0$ and $6$ is $6$ .

$2 \sqrt{5} + 8 \sqrt{5} + 6 \sqrt{2} - \sqrt{5}$

Step 2

Add $2 \sqrt{5}$ and $8 \sqrt{5}$ .

$10 \sqrt{5} + 6 \sqrt{2} - \sqrt{5}$

Step 3

Subtract $\sqrt{5}$ from $10 \sqrt{5}$ .

$9 \sqrt{5} + 6 \sqrt{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$9 \sqrt{5} + 6 \sqrt{2}$

Decimal Form:

$28.60989317 \dots$