Algebra Examples

$2 \sqrt{5} + \sqrt{45} + \sqrt{180} - \sqrt{80}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $45$ as $3^{2} \cdot 5$ .

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Step 1.1.1

Factor $9$ out of $45$ .

$2 \sqrt{5} + \sqrt{9 (5)} + \sqrt{180} - \sqrt{80}$

Step 1.1.2

Rewrite $9$ as $3^{2}$ .

$2 \sqrt{5} + \sqrt{3^{2} \cdot 5} + \sqrt{180} - \sqrt{80}$

Step 1.2

Pull terms out from under the radical.

$2 \sqrt{5} + 3 \sqrt{5} + \sqrt{180} - \sqrt{80}$

Step 1.3

Rewrite $180$ as $6^{2} \cdot 5$ .

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Step 1.3.1

Factor $36$ out of $180$ .

$2 \sqrt{5} + 3 \sqrt{5} + \sqrt{36 (5)} - \sqrt{80}$

Step 1.3.2

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

$2 \sqrt{5} + 3 \sqrt{5} + \sqrt{6^{2} \cdot 5} - \sqrt{80}$

Step 1.4

Pull terms out from under the radical.

$2 \sqrt{5} + 3 \sqrt{5} + 6 \sqrt{5} - \sqrt{80}$

Step 1.5

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

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Step 1.5.1

Factor $16$ out of $80$ .

$2 \sqrt{5} + 3 \sqrt{5} + 6 \sqrt{5} - \sqrt{16 (5)}$

Step 1.5.2

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

$2 \sqrt{5} + 3 \sqrt{5} + 6 \sqrt{5} - \sqrt{4^{2} \cdot 5}$

Step 1.6

Pull terms out from under the radical.

$2 \sqrt{5} + 3 \sqrt{5} + 6 \sqrt{5} - (4 \sqrt{5})$

Step 1.7

Multiply $4$ by $- 1$ .

$2 \sqrt{5} + 3 \sqrt{5} + 6 \sqrt{5} - 4 \sqrt{5}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $2 \sqrt{5}$ and $3 \sqrt{5}$ .

$5 \sqrt{5} + 6 \sqrt{5} - 4 \sqrt{5}$

Step 2.2

Add $5 \sqrt{5}$ and $6 \sqrt{5}$ .

$11 \sqrt{5} - 4 \sqrt{5}$

Step 2.3

Subtract $4 \sqrt{5}$ from $11 \sqrt{5}$ .

$7 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$7 \sqrt{5}$

Decimal Form:

$15.65247584 \dots$