Basic Math Examples

(\sqrt{6} - \sqrt{2}) \sqrt{6} - \sqrt{2}

$(\sqrt{6} - \sqrt{2}) \sqrt{6} - \sqrt{2}$

Step 1

Apply the distributive property.

\sqrt{6} \sqrt{6} - \sqrt{2} \sqrt{6} - \sqrt{2}

$\sqrt{6} \sqrt{6} - \sqrt{2} \sqrt{6} - \sqrt{2}$

Step 2

Combine using the product rule for radicals.

\sqrt{6 \cdot 6} - \sqrt{2} \sqrt{6} - \sqrt{2}

$\sqrt{6 \cdot 6} - \sqrt{2} \sqrt{6} - \sqrt{2}$

Step 3

Multiply

- \sqrt{2} \sqrt{6}

$- \sqrt{2} \sqrt{6}$ .

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Step 3.1

Combine using the product rule for radicals.

\sqrt{6 \cdot 6} - \sqrt{6 \cdot 2} - \sqrt{2}

$\sqrt{6 \cdot 6} - \sqrt{6 \cdot 2} - \sqrt{2}$

Step 3.2

Multiply

6

$6$ by

2

$2$ .

\sqrt{6 \cdot 6} - \sqrt{12} - \sqrt{2}

$\sqrt{6 \cdot 6} - \sqrt{12} - \sqrt{2}$

\sqrt{6 \cdot 6} - \sqrt{12} - \sqrt{2}

$\sqrt{6 \cdot 6} - \sqrt{12} - \sqrt{2}$

Step 4

Simplify each term.

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Step 4.1

Multiply

6

$6$ by

6

$6$ .

\sqrt{36} - \sqrt{12} - \sqrt{2}

$\sqrt{36} - \sqrt{12} - \sqrt{2}$

Step 4.2

Rewrite

36

$36$ as

6^{2}

$6^{2}$ .

\sqrt{6^{2}} - \sqrt{12} - \sqrt{2}

$\sqrt{6^{2}} - \sqrt{12} - \sqrt{2}$

Step 4.3

Pull terms out from under the radical, assuming positive real numbers.

6 - \sqrt{12} - \sqrt{2}

$6 - \sqrt{12} - \sqrt{2}$

Step 4.4

Rewrite

12

$12$ as

2^{2} \cdot 3

$2^{2} \cdot 3$ .

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Step 4.4.1

Factor

4

$4$ out of

12

$12$ .

6 - \sqrt{4 (3)} - \sqrt{2}

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

Step 4.4.2

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

6 - \sqrt{2^{2} \cdot 3} - \sqrt{2}

$6 - \sqrt{2^{2} \cdot 3} - \sqrt{2}$

6 - \sqrt{2^{2} \cdot 3} - \sqrt{2}

$6 - \sqrt{2^{2} \cdot 3} - \sqrt{2}$

Step 4.5

Pull terms out from under the radical.

6 - (2 \sqrt{3}) - \sqrt{2}

$6 - (2 \sqrt{3}) - \sqrt{2}$

Step 4.6

Multiply

2

$2$ by

- 1

$- 1$ .

6 - 2 \sqrt{3} - \sqrt{2}

$6 - 2 \sqrt{3} - \sqrt{2}$

6 - 2 \sqrt{3} - \sqrt{2}

$6 - 2 \sqrt{3} - \sqrt{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

6 - 2 \sqrt{3} - \sqrt{2}

$6 - 2 \sqrt{3} - \sqrt{2}$

Decimal Form:

1.12168482 \dots

$1.12168482 \dots$