Algebra Examples

$3 \sqrt{8} - \sqrt{32} + 3 \sqrt{72} - \sqrt{75}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $8$ as $2^{2} \cdot 2$ .

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Step 1.1.1

Factor $4$ out of $8$ .

$3 \sqrt{4 (2)} - \sqrt{32} + 3 \sqrt{72} - \sqrt{75}$

Step 1.1.2

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

$3 \sqrt{2^{2} \cdot 2} - \sqrt{32} + 3 \sqrt{72} - \sqrt{75}$

Step 1.2

Pull terms out from under the radical.

$3 (2 \sqrt{2}) - \sqrt{32} + 3 \sqrt{72} - \sqrt{75}$

Step 1.3

Multiply $2$ by $3$ .

$6 \sqrt{2} - \sqrt{32} + 3 \sqrt{72} - \sqrt{75}$

Step 1.4

Rewrite $32$ as $4^{2} \cdot 2$ .

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Step 1.4.1

Factor $16$ out of $32$ .

$6 \sqrt{2} - \sqrt{16 (2)} + 3 \sqrt{72} - \sqrt{75}$

Step 1.4.2

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

$6 \sqrt{2} - \sqrt{4^{2} \cdot 2} + 3 \sqrt{72} - \sqrt{75}$

Step 1.5

Pull terms out from under the radical.

$6 \sqrt{2} - (4 \sqrt{2}) + 3 \sqrt{72} - \sqrt{75}$

Step 1.6

Multiply $4$ by $- 1$ .

$6 \sqrt{2} - 4 \sqrt{2} + 3 \sqrt{72} - \sqrt{75}$

Step 1.7

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

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Step 1.7.1

Factor $36$ out of $72$ .

$6 \sqrt{2} - 4 \sqrt{2} + 3 \sqrt{36 (2)} - \sqrt{75}$

Step 1.7.2

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

$6 \sqrt{2} - 4 \sqrt{2} + 3 \sqrt{6^{2} \cdot 2} - \sqrt{75}$

Step 1.8

Pull terms out from under the radical.

$6 \sqrt{2} - 4 \sqrt{2} + 3 (6 \sqrt{2}) - \sqrt{75}$

Step 1.9

Multiply $6$ by $3$ .

$6 \sqrt{2} - 4 \sqrt{2} + 18 \sqrt{2} - \sqrt{75}$

Step 1.10

Rewrite $75$ as $5^{2} \cdot 3$ .

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Step 1.10.1

Factor $25$ out of $75$ .

$6 \sqrt{2} - 4 \sqrt{2} + 18 \sqrt{2} - \sqrt{25 (3)}$

Step 1.10.2

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

$6 \sqrt{2} - 4 \sqrt{2} + 18 \sqrt{2} - \sqrt{5^{2} \cdot 3}$

Step 1.11

Pull terms out from under the radical.

$6 \sqrt{2} - 4 \sqrt{2} + 18 \sqrt{2} - (5 \sqrt{3})$

Step 1.12

Multiply $5$ by $- 1$ .

$6 \sqrt{2} - 4 \sqrt{2} + 18 \sqrt{2} - 5 \sqrt{3}$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $4 \sqrt{2}$ from $6 \sqrt{2}$ .

$2 \sqrt{2} + 18 \sqrt{2} - 5 \sqrt{3}$

Step 2.2

Add $2 \sqrt{2}$ and $18 \sqrt{2}$ .

$20 \sqrt{2} - 5 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$20 \sqrt{2} - 5 \sqrt{3}$

Decimal Form:

$19.62401720 \dots$