Finite Math Examples

$\sqrt{10} (\sqrt{5} - \sqrt{6})$

Step 1

Apply the distributive property.

$\sqrt{10} \sqrt{5} + \sqrt{10} (- \sqrt{6})$

Step 2

Combine using the product rule for radicals.

$\sqrt{10 \cdot 5} + \sqrt{10} (- \sqrt{6})$

Step 3

Multiply $\sqrt{10} (- \sqrt{6})$ .

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Step 3.1

Combine using the product rule for radicals.

$\sqrt{10 \cdot 5} - \sqrt{10 \cdot 6}$

Step 3.2

Multiply $10$ by $6$ .

$\sqrt{10 \cdot 5} - \sqrt{60}$

$\sqrt{10 \cdot 5} - \sqrt{60}$

Step 4

Simplify each term.

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Step 4.1

Multiply $10$ by $5$ .

$\sqrt{50} - \sqrt{60}$

Step 4.2

Rewrite $50$ as $5^{2} \cdot 2$ .

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Step 4.2.1

Factor $25$ out of $50$ .

$\sqrt{25 (2)} - \sqrt{60}$

Step 4.2.2

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2} \cdot 2} - \sqrt{60}$

$\sqrt{5^{2} \cdot 2} - \sqrt{60}$

Step 4.3

Pull terms out from under the radical.

$5 \sqrt{2} - \sqrt{60}$

Step 4.4

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

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Step 4.4.1

Factor $4$ out of $60$ .

$5 \sqrt{2} - \sqrt{4 (15)}$

Step 4.4.2

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

$5 \sqrt{2} - \sqrt{2^{2} \cdot 15}$

$5 \sqrt{2} - \sqrt{2^{2} \cdot 15}$

Step 4.5

Pull terms out from under the radical.

$5 \sqrt{2} - (2 \sqrt{15})$

Step 4.6

Multiply $2$ by $- 1$ .

$5 \sqrt{2} - 2 \sqrt{15}$

$5 \sqrt{2} - 2 \sqrt{15}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt{2} - 2 \sqrt{15}$

Decimal Form:

$- 0.67489888 \dots$

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