Basic Math Examples

$- 3 \sqrt{6} (5 - 8 \sqrt{2}) - \sqrt{6}$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$- 3 \sqrt{6} \cdot 5 - 3 \sqrt{6} (- 8 \sqrt{2}) - \sqrt{6}$

Step 1.2

Multiply $5$ by $- 3$ .

$- 15 \sqrt{6} - 3 \sqrt{6} (- 8 \sqrt{2}) - \sqrt{6}$

Step 1.3

Multiply $- 3 \sqrt{6} (- 8 \sqrt{2})$ .

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Step 1.3.1

Multiply $- 8$ by $- 3$ .

$- 15 \sqrt{6} + 24 \sqrt{6} \sqrt{2} - \sqrt{6}$

Step 1.3.2

Combine using the product rule for radicals.

$- 15 \sqrt{6} + 24 \sqrt{2 \cdot 6} - \sqrt{6}$

Step 1.3.3

Multiply $2$ by $6$ .

$- 15 \sqrt{6} + 24 \sqrt{12} - \sqrt{6}$

Step 1.4

Simplify each term.

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Step 1.4.1

Rewrite $12$ as $2^{2} \cdot 3$ .

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Step 1.4.1.1

Factor $4$ out of $12$ .

$- 15 \sqrt{6} + 24 \sqrt{4 (3)} - \sqrt{6}$

Step 1.4.1.2

Rewrite $4$ as $2^{2}$ .

$- 15 \sqrt{6} + 24 \sqrt{2^{2} \cdot 3} - \sqrt{6}$

Step 1.4.2

Pull terms out from under the radical.

$- 15 \sqrt{6} + 24 (2 \sqrt{3}) - \sqrt{6}$

Step 1.4.3

Multiply $2$ by $24$ .

$- 15 \sqrt{6} + 48 \sqrt{3} - \sqrt{6}$

Step 2

Subtract $\sqrt{6}$ from $- 15 \sqrt{6}$ .

$- 16 \sqrt{6} + 48 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 16 \sqrt{6} + 48 \sqrt{3}$

Decimal Form:

$43.94660287 \dots$