Finite Math Examples

$(\sqrt{5} + \sqrt{70}) (\sqrt{14} + \sqrt{7})$

Step 1

Simplify and reorder the polynomial.

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Step 1.1

Expand $(\sqrt{5} + \sqrt{70}) (\sqrt{14} + \sqrt{7})$ using the FOIL Method.

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Step 1.1.1

Apply the distributive property.

$\sqrt{5} (\sqrt{14} + \sqrt{7}) + \sqrt{70} (\sqrt{14} + \sqrt{7})$

Step 1.1.2

Apply the distributive property.

$\sqrt{5} \sqrt{14} + \sqrt{5} \sqrt{7} + \sqrt{70} (\sqrt{14} + \sqrt{7})$

Step 1.1.3

Apply the distributive property.

$\sqrt{5} \sqrt{14} + \sqrt{5} \sqrt{7} + \sqrt{70} \sqrt{14} + \sqrt{70} \sqrt{7}$

Step 1.2

Simplify each term.

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Step 1.2.1

Combine using the product rule for radicals.

$\sqrt{5 \cdot 14} + \sqrt{5} \sqrt{7} + \sqrt{70} \sqrt{14} + \sqrt{70} \sqrt{7}$

Step 1.2.2

Multiply $5$ by $14$ .

$\sqrt{70} + \sqrt{5} \sqrt{7} + \sqrt{70} \sqrt{14} + \sqrt{70} \sqrt{7}$

Step 1.2.3

Combine using the product rule for radicals.

$\sqrt{70} + \sqrt{5 \cdot 7} + \sqrt{70} \sqrt{14} + \sqrt{70} \sqrt{7}$

Step 1.2.4

Multiply $5$ by $7$ .

$\sqrt{70} + \sqrt{35} + \sqrt{70} \sqrt{14} + \sqrt{70} \sqrt{7}$

Step 1.2.5

Combine using the product rule for radicals.

$\sqrt{70} + \sqrt{35} + \sqrt{70 \cdot 14} + \sqrt{70} \sqrt{7}$

Step 1.2.6

Multiply $70$ by $14$ .

$\sqrt{70} + \sqrt{35} + \sqrt{980} + \sqrt{70} \sqrt{7}$

Step 1.2.7

Rewrite $980$ as $14^{2} \cdot 5$ .

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Step 1.2.7.1

Factor $196$ out of $980$ .

$\sqrt{70} + \sqrt{35} + \sqrt{196 (5)} + \sqrt{70} \sqrt{7}$

Step 1.2.7.2

Rewrite $196$ as $14^{2}$ .

$\sqrt{70} + \sqrt{35} + \sqrt{14^{2} \cdot 5} + \sqrt{70} \sqrt{7}$

Step 1.2.8

Pull terms out from under the radical.

$\sqrt{70} + \sqrt{35} + 14 \sqrt{5} + \sqrt{70} \sqrt{7}$

Step 1.2.9

Combine using the product rule for radicals.

$\sqrt{70} + \sqrt{35} + 14 \sqrt{5} + \sqrt{70 \cdot 7}$

Step 1.2.10

Multiply $70$ by $7$ .

$\sqrt{70} + \sqrt{35} + 14 \sqrt{5} + \sqrt{490}$

Step 1.2.11

Rewrite $490$ as $7^{2} \cdot 10$ .

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Step 1.2.11.1

Factor $49$ out of $490$ .

$\sqrt{70} + \sqrt{35} + 14 \sqrt{5} + \sqrt{49 (10)}$

Step 1.2.11.2

Rewrite $49$ as $7^{2}$ .

$\sqrt{70} + \sqrt{35} + 14 \sqrt{5} + \sqrt{7^{2} \cdot 10}$

Step 1.2.12

Pull terms out from under the radical.

$\sqrt{70} + \sqrt{35} + 14 \sqrt{5} + 7 \sqrt{10}$

Step 2

The expression is constant, which means it can be rewritten with a factor of $x^{0}$ . The degree is the largest exponent on the variable.

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