Trigonometry Examples

$\sqrt{10} (- 2 \sqrt{15} + \sqrt{10})$

Step 1

Apply the distributive property.

$\sqrt{10} (- 2 \sqrt{15}) + \sqrt{10} \sqrt{10}$

Step 2

Multiply $\sqrt{10} (- 2 \sqrt{15})$ .

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Step 2.1

Combine using the product rule for radicals.

$- 2 \sqrt{10 \cdot 15} + \sqrt{10} \sqrt{10}$

Step 2.2

Multiply $10$ by $15$ .

$- 2 \sqrt{150} + \sqrt{10} \sqrt{10}$

$- 2 \sqrt{150} + \sqrt{10} \sqrt{10}$

Step 3

Combine using the product rule for radicals.

$- 2 \sqrt{150} + \sqrt{10 \cdot 10}$

Step 4

Simplify each term.

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Step 4.1

Rewrite $150$ as $5^{2} \cdot 6$ .

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Step 4.1.1

Factor $25$ out of $150$ .

$- 2 \sqrt{25 (6)} + \sqrt{10 \cdot 10}$

Step 4.1.2

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

$- 2 \sqrt{5^{2} \cdot 6} + \sqrt{10 \cdot 10}$

$- 2 \sqrt{5^{2} \cdot 6} + \sqrt{10 \cdot 10}$

Step 4.2

Pull terms out from under the radical.

$- 2 (5 \sqrt{6}) + \sqrt{10 \cdot 10}$

Step 4.3

Multiply $5$ by $- 2$ .

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

Step 4.4

Multiply $10$ by $10$ .

$- 10 \sqrt{6} + \sqrt{100}$

Step 4.5

Rewrite $100$ as $10^{2}$ .

$- 10 \sqrt{6} + \sqrt{10^{2}}$

Step 4.6

Pull terms out from under the radical, assuming positive real numbers.

$- 10 \sqrt{6} + 10$

$- 10 \sqrt{6} + 10$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- 10 \sqrt{6} + 10$

Decimal Form:

$- 14.49489742 \dots$

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