Finite Math Examples

$(\sqrt{6} + 2) (\sqrt{42} - 4)$

Step 1

Expand $(\sqrt{6} + 2) (\sqrt{42} - 4)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$\sqrt{6} (\sqrt{42} - 4) + 2 (\sqrt{42} - 4)$

Step 1.2

Apply the distributive property.

$\sqrt{6} \sqrt{42} + \sqrt{6} \cdot - 4 + 2 (\sqrt{42} - 4)$

Step 1.3

Apply the distributive property.

$\sqrt{6} \sqrt{42} + \sqrt{6} \cdot - 4 + 2 \sqrt{42} + 2 \cdot - 4$

Step 2

Simplify each term.

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Step 2.1

Combine using the product rule for radicals.

$\sqrt{6 \cdot 42} + \sqrt{6} \cdot - 4 + 2 \sqrt{42} + 2 \cdot - 4$

Step 2.2

Multiply $6$ by $42$ .

$\sqrt{252} + \sqrt{6} \cdot - 4 + 2 \sqrt{42} + 2 \cdot - 4$

Step 2.3

Rewrite $252$ as $6^{2} \cdot 7$ .

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Step 2.3.1

Factor $36$ out of $252$ .

$\sqrt{36 (7)} + \sqrt{6} \cdot - 4 + 2 \sqrt{42} + 2 \cdot - 4$

Step 2.3.2

Rewrite $36$ as $6^{2}$ .

$\sqrt{6^{2} \cdot 7} + \sqrt{6} \cdot - 4 + 2 \sqrt{42} + 2 \cdot - 4$

Step 2.4

Pull terms out from under the radical.

$6 \sqrt{7} + \sqrt{6} \cdot - 4 + 2 \sqrt{42} + 2 \cdot - 4$

Step 2.5

Move $- 4$ to the left of $\sqrt{6}$ .

$6 \sqrt{7} - 4 \cdot \sqrt{6} + 2 \sqrt{42} + 2 \cdot - 4$

Step 2.6

Multiply $2$ by $- 4$ .

$6 \sqrt{7} - 4 \sqrt{6} + 2 \sqrt{42} - 8$

Step 3

The result can be shown in multiple forms.

Exact Form:

$6 \sqrt{7} - 4 \sqrt{6} + 2 \sqrt{42} - 8$

Decimal Form:

$11.03803029 \dots$