Pre-Algebra Examples

$2 \sqrt{6} (\sqrt{7} - \sqrt{2})$

Step 1

Apply the distributive property.

$2 \sqrt{6} \sqrt{7} + 2 \sqrt{6} (- \sqrt{2})$

Step 2

Multiply $2 \sqrt{6} \sqrt{7}$ .

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Step 2.1

Combine using the product rule for radicals.

$2 \sqrt{7 \cdot 6} + 2 \sqrt{6} (- \sqrt{2})$

Step 2.2

Multiply $7$ by $6$ .

$2 \sqrt{42} + 2 \sqrt{6} (- \sqrt{2})$

$2 \sqrt{42} + 2 \sqrt{6} (- \sqrt{2})$

Step 3

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

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Step 3.1

Multiply $- 1$ by $2$ .

$2 \sqrt{42} - 2 \sqrt{6} \sqrt{2}$

Step 3.2

Combine using the product rule for radicals.

$2 \sqrt{42} - 2 \sqrt{2 \cdot 6}$

Step 3.3

Multiply $2$ by $6$ .

$2 \sqrt{42} - 2 \sqrt{12}$

$2 \sqrt{42} - 2 \sqrt{12}$

Step 4

Simplify each term.

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Step 4.1

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

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Step 4.1.1

Factor $4$ out of $12$ .

$2 \sqrt{42} - 2 \sqrt{4 (3)}$

Step 4.1.2

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

$2 \sqrt{42} - 2 \sqrt{2^{2} \cdot 3}$

$2 \sqrt{42} - 2 \sqrt{2^{2} \cdot 3}$

Step 4.2

Pull terms out from under the radical.

$2 \sqrt{42} - 2 (2 \sqrt{3})$

Step 4.3

Multiply $2$ by $- 2$ .

$2 \sqrt{42} - 4 \sqrt{3}$

$2 \sqrt{42} - 4 \sqrt{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{42} - 4 \sqrt{3}$

Decimal Form:

$6.03327816 \dots$

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