Trigonometry Examples

${(\sqrt{13} - 6)}^{2}$

Step 1

Rewrite ${(\sqrt{13} - 6)}^{2}$ as $(\sqrt{13} - 6) (\sqrt{13} - 6)$ .

$(\sqrt{13} - 6) (\sqrt{13} - 6)$

Step 2

Expand $(\sqrt{13} - 6) (\sqrt{13} - 6)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$\sqrt{13} (\sqrt{13} - 6) - 6 (\sqrt{13} - 6)$

Step 2.2

Apply the distributive property.

$\sqrt{13} \sqrt{13} + \sqrt{13} \cdot - 6 - 6 (\sqrt{13} - 6)$

Step 2.3

Apply the distributive property.

$\sqrt{13} \sqrt{13} + \sqrt{13} \cdot - 6 - 6 \sqrt{13} - 6 \cdot - 6$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Combine using the product rule for radicals.

$\sqrt{13 \cdot 13} + \sqrt{13} \cdot - 6 - 6 \sqrt{13} - 6 \cdot - 6$

Step 3.1.2

Multiply $13$ by $13$ .

$\sqrt{169} + \sqrt{13} \cdot - 6 - 6 \sqrt{13} - 6 \cdot - 6$

Step 3.1.3

Rewrite $169$ as $13^{2}$ .

$\sqrt{13^{2}} + \sqrt{13} \cdot - 6 - 6 \sqrt{13} - 6 \cdot - 6$

Step 3.1.4

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

$13 + \sqrt{13} \cdot - 6 - 6 \sqrt{13} - 6 \cdot - 6$

Step 3.1.5

Move $- 6$ to the left of $\sqrt{13}$ .

$13 - 6 \cdot \sqrt{13} - 6 \sqrt{13} - 6 \cdot - 6$

Step 3.1.6

Multiply $- 6$ by $- 6$ .

$13 - 6 \sqrt{13} - 6 \sqrt{13} + 36$

Step 3.2

Add $13$ and $36$ .

$49 - 6 \sqrt{13} - 6 \sqrt{13}$

Step 3.3

Subtract $6 \sqrt{13}$ from $- 6 \sqrt{13}$ .

$49 - 12 \sqrt{13}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$49 - 12 \sqrt{13}$

Decimal Form:

$5.73338469 \dots$