Finite Math Examples

$\sqrt{6} (\sqrt{3} + 5 \sqrt{2})$

Step 1

Apply the distributive property.

$\sqrt{6} \sqrt{3} + \sqrt{6} (5 \sqrt{2})$

Step 2

Combine using the product rule for radicals.

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

Step 3

Multiply $\sqrt{6} (5 \sqrt{2})$ .

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Step 3.1

Combine using the product rule for radicals.

$\sqrt{6 \cdot 3} + 5 \sqrt{6 \cdot 2}$

Step 3.2

Multiply $6$ by $2$ .

$\sqrt{6 \cdot 3} + 5 \sqrt{12}$

$\sqrt{6 \cdot 3} + 5 \sqrt{12}$

Step 4

Simplify each term.

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Step 4.1

Multiply $6$ by $3$ .

$\sqrt{18} + 5 \sqrt{12}$

Step 4.2

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

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Step 4.2.1

Factor $9$ out of $18$ .

$\sqrt{9 (2)} + 5 \sqrt{12}$

Step 4.2.2

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

$\sqrt{3^{2} \cdot 2} + 5 \sqrt{12}$

$\sqrt{3^{2} \cdot 2} + 5 \sqrt{12}$

Step 4.3

Pull terms out from under the radical.

$3 \sqrt{2} + 5 \sqrt{12}$

Step 4.4

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

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Step 4.4.1

Factor $4$ out of $12$ .

$3 \sqrt{2} + 5 \sqrt{4 (3)}$

Step 4.4.2

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

$3 \sqrt{2} + 5 \sqrt{2^{2} \cdot 3}$

$3 \sqrt{2} + 5 \sqrt{2^{2} \cdot 3}$

Step 4.5

Pull terms out from under the radical.

$3 \sqrt{2} + 5 (2 \sqrt{3})$

Step 4.6

Multiply $2$ by $5$ .

$3 \sqrt{2} + 10 \sqrt{3}$

$3 \sqrt{2} + 10 \sqrt{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{2} + 10 \sqrt{3}$

Decimal Form:

$21.56314876 \dots$

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