Finite Math Examples

$3 \sqrt{6} (\sqrt{10} - \sqrt{3})$

Step 1

Apply the distributive property.

$3 \sqrt{6} \sqrt{10} + 3 \sqrt{6} (- \sqrt{3})$

Step 2

Multiply $3 \sqrt{6} \sqrt{10}$ .

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Step 2.1

Combine using the product rule for radicals.

$3 \sqrt{10 \cdot 6} + 3 \sqrt{6} (- \sqrt{3})$

Step 2.2

Multiply $10$ by $6$ .

$3 \sqrt{60} + 3 \sqrt{6} (- \sqrt{3})$

$3 \sqrt{60} + 3 \sqrt{6} (- \sqrt{3})$

Step 3

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

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Step 3.1

Multiply $- 1$ by $3$ .

$3 \sqrt{60} - 3 \sqrt{6} \sqrt{3}$

Step 3.2

Combine using the product rule for radicals.

$3 \sqrt{60} - 3 \sqrt{3 \cdot 6}$

Step 3.3

Multiply $3$ by $6$ .

$3 \sqrt{60} - 3 \sqrt{18}$

$3 \sqrt{60} - 3 \sqrt{18}$

Step 4

Simplify each term.

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Step 4.1

Rewrite $60$ as $2^{2} \cdot 15$ .

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Step 4.1.1

Factor $4$ out of $60$ .

$3 \sqrt{4 (15)} - 3 \sqrt{18}$

Step 4.1.2

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

$3 \sqrt{2^{2} \cdot 15} - 3 \sqrt{18}$

$3 \sqrt{2^{2} \cdot 15} - 3 \sqrt{18}$

Step 4.2

Pull terms out from under the radical.

$3 (2 \sqrt{15}) - 3 \sqrt{18}$

Step 4.3

Multiply $2$ by $3$ .

$6 \sqrt{15} - 3 \sqrt{18}$

Step 4.4

Rewrite $18$ as $3^{2} \cdot 2$ .

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Step 4.4.1

Factor $9$ out of $18$ .

$6 \sqrt{15} - 3 \sqrt{9 (2)}$

Step 4.4.2

Rewrite $9$ as $3^{2}$ .

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

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

Step 4.5

Pull terms out from under the radical.

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

Step 4.6

Multiply $3$ by $- 3$ .

$6 \sqrt{15} - 9 \sqrt{2}$

$6 \sqrt{15} - 9 \sqrt{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$6 \sqrt{15} - 9 \sqrt{2}$

Decimal Form:

$10.50997801 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$