Basic Math Examples

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

Step 1

Apply the distributive property.

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

Step 2

Combine using the product rule for radicals.

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

Step 3

Multiply $\sqrt{2} (- \sqrt{3})$ .

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Step 3.1

Combine using the product rule for radicals.

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

Step 3.2

Multiply $2$ by $3$ .

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

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

Step 4

Simplify each term.

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Step 4.1

Multiply $2$ by $6$ .

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

Step 4.2

Rewrite $12$ as $2^{2} \cdot 3$ .

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Step 4.2.1

Factor $4$ out of $12$ .

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

Step 4.2.2

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

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

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

Step 4.3

Pull terms out from under the radical.

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

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$1.01461187 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$