Trigonometry Examples

$(7 + \sqrt{10}) (7 + \sqrt{10})$

Step 1

Expand $(7 + \sqrt{10}) (7 + \sqrt{10})$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$7 (7 + \sqrt{10}) + \sqrt{10} (7 + \sqrt{10})$

Step 1.2

Apply the distributive property.

$7 \cdot 7 + 7 \sqrt{10} + \sqrt{10} (7 + \sqrt{10})$

Step 1.3

Apply the distributive property.

$7 \cdot 7 + 7 \sqrt{10} + \sqrt{10} \cdot 7 + \sqrt{10} \sqrt{10}$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $7$ by $7$ .

$49 + 7 \sqrt{10} + \sqrt{10} \cdot 7 + \sqrt{10} \sqrt{10}$

Step 2.1.2

Move $7$ to the left of $\sqrt{10}$ .

$49 + 7 \sqrt{10} + 7 \cdot \sqrt{10} + \sqrt{10} \sqrt{10}$

Step 2.1.3

Combine using the product rule for radicals.

$49 + 7 \sqrt{10} + 7 \sqrt{10} + \sqrt{10 \cdot 10}$

Step 2.1.4

Multiply $10$ by $10$ .

$49 + 7 \sqrt{10} + 7 \sqrt{10} + \sqrt{100}$

Step 2.1.5

Rewrite $100$ as $10^{2}$ .

$49 + 7 \sqrt{10} + 7 \sqrt{10} + \sqrt{10^{2}}$

Step 2.1.6

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

$49 + 7 \sqrt{10} + 7 \sqrt{10} + 10$

Step 2.2

Add $49$ and $10$ .

$59 + 7 \sqrt{10} + 7 \sqrt{10}$

Step 2.3

Add $7 \sqrt{10}$ and $7 \sqrt{10}$ .

$59 + 14 \sqrt{10}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$59 + 14 \sqrt{10}$

Decimal Form:

$103.27188724 \dots$