Basic Math Examples

$8 \sqrt{75} - 4 \sqrt{8} - 4 \sqrt{27}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $25$ out of $75$ .

$8 \sqrt{25 (3)} - 4 \sqrt{8} - 4 \sqrt{27}$

Step 1.1.2

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

$8 \sqrt{5^{2} \cdot 3} - 4 \sqrt{8} - 4 \sqrt{27}$

Step 1.2

Pull terms out from under the radical.

$8 (5 \sqrt{3}) - 4 \sqrt{8} - 4 \sqrt{27}$

Step 1.3

Multiply $5$ by $8$ .

$40 \sqrt{3} - 4 \sqrt{8} - 4 \sqrt{27}$

Step 1.4

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

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Step 1.4.1

Factor $4$ out of $8$ .

$40 \sqrt{3} - 4 \sqrt{4 (2)} - 4 \sqrt{27}$

Step 1.4.2

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

$40 \sqrt{3} - 4 \sqrt{2^{2} \cdot 2} - 4 \sqrt{27}$

Step 1.5

Pull terms out from under the radical.

$40 \sqrt{3} - 4 (2 \sqrt{2}) - 4 \sqrt{27}$

Step 1.6

Multiply $2$ by $- 4$ .

$40 \sqrt{3} - 8 \sqrt{2} - 4 \sqrt{27}$

Step 1.7

Rewrite $27$ as $3^{2} \cdot 3$ .

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Step 1.7.1

Factor $9$ out of $27$ .

$40 \sqrt{3} - 8 \sqrt{2} - 4 \sqrt{9 (3)}$

Step 1.7.2

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

$40 \sqrt{3} - 8 \sqrt{2} - 4 \sqrt{3^{2} \cdot 3}$

Step 1.8

Pull terms out from under the radical.

$40 \sqrt{3} - 8 \sqrt{2} - 4 (3 \sqrt{3})$

Step 1.9

Multiply $3$ by $- 4$ .

$40 \sqrt{3} - 8 \sqrt{2} - 12 \sqrt{3}$

Step 2

Subtract $12 \sqrt{3}$ from $40 \sqrt{3}$ .

$28 \sqrt{3} - 8 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$28 \sqrt{3} - 8 \sqrt{2}$

Decimal Form:

$37.18371411 \dots$