Algebra Examples

$(4 - \sqrt{50}) + (7 + 3 \sqrt{18}) - (12 - 2 \sqrt{72})$

Step 1

Remove parentheses.

$4 - \sqrt{50} + 7 + 3 \sqrt{18} - (12 - 2 \sqrt{72})$

Step 2

Simplify each term.

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Step 2.1

Rewrite $50$ as $5^{2} \cdot 2$ .

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Step 2.1.1

Factor $25$ out of $50$ .

$4 - \sqrt{25 (2)} + 7 + 3 \sqrt{18} - (12 - 2 \sqrt{72})$

Step 2.1.2

Rewrite $25$ as $5^{2}$ .

$4 - \sqrt{5^{2} \cdot 2} + 7 + 3 \sqrt{18} - (12 - 2 \sqrt{72})$

Step 2.2

Pull terms out from under the radical.

$4 - (5 \sqrt{2}) + 7 + 3 \sqrt{18} - (12 - 2 \sqrt{72})$

Step 2.3

Multiply $5$ by $- 1$ .

$4 - 5 \sqrt{2} + 7 + 3 \sqrt{18} - (12 - 2 \sqrt{72})$

Step 2.4

Rewrite $18$ as $3^{2} \cdot 2$ .

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Step 2.4.1

Factor $9$ out of $18$ .

$4 - 5 \sqrt{2} + 7 + 3 \sqrt{9 (2)} - (12 - 2 \sqrt{72})$

Step 2.4.2

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

$4 - 5 \sqrt{2} + 7 + 3 \sqrt{3^{2} \cdot 2} - (12 - 2 \sqrt{72})$

Step 2.5

Pull terms out from under the radical.

$4 - 5 \sqrt{2} + 7 + 3 (3 \sqrt{2}) - (12 - 2 \sqrt{72})$

Step 2.6

Multiply $3$ by $3$ .

$4 - 5 \sqrt{2} + 7 + 9 \sqrt{2} - (12 - 2 \sqrt{72})$

Step 2.7

Simplify each term.

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Step 2.7.1

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

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Step 2.7.1.1

Factor $36$ out of $72$ .

$4 - 5 \sqrt{2} + 7 + 9 \sqrt{2} - (12 - 2 \sqrt{36 (2)})$

Step 2.7.1.2

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

$4 - 5 \sqrt{2} + 7 + 9 \sqrt{2} - (12 - 2 \sqrt{6^{2} \cdot 2})$

Step 2.7.2

Pull terms out from under the radical.

$4 - 5 \sqrt{2} + 7 + 9 \sqrt{2} - (12 - 2 (6 \sqrt{2}))$

Step 2.7.3

Multiply $6$ by $- 2$ .

$4 - 5 \sqrt{2} + 7 + 9 \sqrt{2} - (12 - 12 \sqrt{2})$

Step 2.8

Apply the distributive property.

$4 - 5 \sqrt{2} + 7 + 9 \sqrt{2} - 1 \cdot 12 - (- 12 \sqrt{2})$

Step 2.9

Multiply $- 1$ by $12$ .

$4 - 5 \sqrt{2} + 7 + 9 \sqrt{2} - 12 - (- 12 \sqrt{2})$

Step 2.10

Multiply $- 12$ by $- 1$ .

$4 - 5 \sqrt{2} + 7 + 9 \sqrt{2} - 12 + 12 \sqrt{2}$

Step 3

Simplify by adding terms.

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Step 3.1

Add $4$ and $7$ .

$11 - 5 \sqrt{2} + 9 \sqrt{2} - 12 + 12 \sqrt{2}$

Step 3.2

Subtract $12$ from $11$ .

$- 1 - 5 \sqrt{2} + 9 \sqrt{2} + 12 \sqrt{2}$

Step 3.3

Add $- 5 \sqrt{2}$ and $9 \sqrt{2}$ .

$- 1 + 4 \sqrt{2} + 12 \sqrt{2}$

Step 3.4

Add $4 \sqrt{2}$ and $12 \sqrt{2}$ .

$- 1 + 16 \sqrt{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- 1 + 16 \sqrt{2}$

Decimal Form:

$21.62741699 \dots$