Trigonometry Examples

$4 \sqrt{10} (\sqrt{3} - 3 \sqrt{11})$

Step 1

Apply the distributive property.

$4 \sqrt{10} \sqrt{3} + 4 \sqrt{10} (- 3 \sqrt{11})$

Step 2

Multiply $4 \sqrt{10} \sqrt{3}$ .

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Step 2.1

Combine using the product rule for radicals.

$4 \sqrt{3 \cdot 10} + 4 \sqrt{10} (- 3 \sqrt{11})$

Step 2.2

Multiply $3$ by $10$ .

$4 \sqrt{30} + 4 \sqrt{10} (- 3 \sqrt{11})$

Step 3

Multiply $4 \sqrt{10} (- 3 \sqrt{11})$ .

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Step 3.1

Multiply $- 3$ by $4$ .

$4 \sqrt{30} - 12 \sqrt{10} \sqrt{11}$

Step 3.2

Combine using the product rule for radicals.

$4 \sqrt{30} - 12 \sqrt{11 \cdot 10}$

Step 3.3

Multiply $11$ by $10$ .

$4 \sqrt{30} - 12 \sqrt{110}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{30} - 12 \sqrt{110}$

Decimal Form:

$- 103.94815948 \dots$