Basic Math Examples

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

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

Step 1

Simplify each term.

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Step 1.1

Rewrite

75

$75$ as

5^{2} \cdot 3

$5^{2} \cdot 3$ .

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Step 1.1.1

Factor

25

$25$ out of

75

$75$ .

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

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

Step 1.1.2

Rewrite

25

$25$ as

5^{2}

$5^{2}$ .

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

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

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

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

Step 1.2

Pull terms out from under the radical.

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

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

Step 1.3

Multiply

5

$5$ by

8

$8$ .

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

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

Step 1.4

Rewrite

8

$8$ as

2^{2} \cdot 2

$2^{2} \cdot 2$ .

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Step 1.4.1

Factor

4

$4$ out of

8

$8$ .

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

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

Step 1.4.2

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

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

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

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

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

Step 1.5

Pull terms out from under the radical.

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

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

Step 1.6

Multiply

2

$2$ by

- 4

$- 4$ .

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

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

Step 1.7

Rewrite

27

$27$ as

3^{2} \cdot 3

$3^{2} \cdot 3$ .

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Step 1.7.1

Factor

9

$9$ out of

27

$27$ .

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

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

Step 1.7.2

Rewrite

9

$9$ as

3^{2}

$3^{2}$ .

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

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

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

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

Step 1.8

Pull terms out from under the radical.

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

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

Step 1.9

Multiply

3

$3$ by

- 4

$- 4$ .

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

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

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

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

Step 2

Subtract

12 \sqrt{3}

$12 \sqrt{3}$ from

40 \sqrt{3}

$40 \sqrt{3}$ .

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

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

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

Decimal Form:

37.18371411 \dots

$37.18371411 \dots$