Algebra Examples

$2 \sqrt{80} - \sqrt{45} - 4 \sqrt{30} \div 2 \sqrt{6}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $16$ out of $80$ .

$2 \sqrt{16 (5)} - \sqrt{45} - 4 \sqrt{30} \div 2 \sqrt{6}$

Step 1.1.2

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

$2 \sqrt{4^{2} \cdot 5} - \sqrt{45} - 4 \sqrt{30} \div 2 \sqrt{6}$

Step 1.2

Pull terms out from under the radical.

$2 (4 \sqrt{5}) - \sqrt{45} - 4 \sqrt{30} \div 2 \sqrt{6}$

Step 1.3

Multiply $4$ by $2$ .

$8 \sqrt{5} - \sqrt{45} - 4 \sqrt{30} \div 2 \sqrt{6}$

Step 1.4

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

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Step 1.4.1

Factor $9$ out of $45$ .

$8 \sqrt{5} - \sqrt{9 (5)} - 4 \sqrt{30} \div 2 \sqrt{6}$

Step 1.4.2

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

$8 \sqrt{5} - \sqrt{3^{2} \cdot 5} - 4 \sqrt{30} \div 2 \sqrt{6}$

Step 1.5

Pull terms out from under the radical.

$8 \sqrt{5} - (3 \sqrt{5}) - 4 \sqrt{30} \div 2 \sqrt{6}$

Step 1.6

Multiply $3$ by $- 1$ .

$8 \sqrt{5} - 3 \sqrt{5} - 4 \sqrt{30} \div 2 \sqrt{6}$

Step 1.7

Rewrite the division as a fraction.

$8 \sqrt{5} - 3 \sqrt{5} - \frac{4 \sqrt{30}}{2 \sqrt{6}}$

Step 1.8

Cancel the common factor of $4$ and $2$ .

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Step 1.8.1

Factor $2$ out of $4 \sqrt{30}$ .

$8 \sqrt{5} - 3 \sqrt{5} - \frac{2 (2 \sqrt{30})}{2 \sqrt{6}}$

Step 1.8.2

Cancel the common factors.

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Step 1.8.2.1

Factor $2$ out of $2 \sqrt{6}$ .

$8 \sqrt{5} - 3 \sqrt{5} - \frac{2 (2 \sqrt{30})}{2 (\sqrt{6})}$

Step 1.8.2.2

Cancel the common factor.

$8 \sqrt{5} - 3 \sqrt{5} - \frac{2 (2 \sqrt{30})}{2 \sqrt{6}}$

Step 1.8.2.3

Rewrite the expression.

$8 \sqrt{5} - 3 \sqrt{5} - \frac{2 \sqrt{30}}{\sqrt{6}}$

Step 1.9

Combine $\sqrt{30}$ and $\sqrt{6}$ into a single radical.

$8 \sqrt{5} - 3 \sqrt{5} - (2 \sqrt{\frac{30}{6}})$

Step 1.10

Divide $30$ by $6$ .

$8 \sqrt{5} - 3 \sqrt{5} - (2 \sqrt{5})$

Step 1.11

Multiply $2$ by $- 1$ .

$8 \sqrt{5} - 3 \sqrt{5} - 2 \sqrt{5}$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $3 \sqrt{5}$ from $8 \sqrt{5}$ .

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

Step 2.2

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

$3 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{5}$

Decimal Form:

$6.70820393 \dots$