Finite Math Examples

$9 \sqrt{2} (\sqrt{15} + \sqrt{14})$

Step 1

Apply the distributive property.

$9 \sqrt{2} \sqrt{15} + 9 \sqrt{2} \sqrt{14}$

Step 2

Multiply $9 \sqrt{2} \sqrt{15}$ .

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Step 2.1

Combine using the product rule for radicals.

$9 \sqrt{15 \cdot 2} + 9 \sqrt{2} \sqrt{14}$

Step 2.2

Multiply $15$ by $2$ .

$9 \sqrt{30} + 9 \sqrt{2} \sqrt{14}$

$9 \sqrt{30} + 9 \sqrt{2} \sqrt{14}$

Step 3

Multiply $9 \sqrt{2} \sqrt{14}$ .

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Step 3.1

Combine using the product rule for radicals.

$9 \sqrt{30} + 9 \sqrt{14 \cdot 2}$

Step 3.2

Multiply $14$ by $2$ .

$9 \sqrt{30} + 9 \sqrt{28}$

$9 \sqrt{30} + 9 \sqrt{28}$

Step 4

Simplify each term.

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Step 4.1

Rewrite $28$ as $2^{2} \cdot 7$ .

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Step 4.1.1

Factor $4$ out of $28$ .

$9 \sqrt{30} + 9 \sqrt{4 (7)}$

Step 4.1.2

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

$9 \sqrt{30} + 9 \sqrt{2^{2} \cdot 7}$

$9 \sqrt{30} + 9 \sqrt{2^{2} \cdot 7}$

Step 4.2

Pull terms out from under the radical.

$9 \sqrt{30} + 9 (2 \sqrt{7})$

Step 4.3

Multiply $2$ by $9$ .

$9 \sqrt{30} + 18 \sqrt{7}$

$9 \sqrt{30} + 18 \sqrt{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$9 \sqrt{30} + 18 \sqrt{7}$

Decimal Form:

$96.91855377 \dots$

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