Trigonometry Examples

$\sqrt{10} (5 \sqrt{50} - 6 \sqrt{2})$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $25$ out of $50$ .

$\sqrt{10} (5 \sqrt{25 (2)} - 6 \sqrt{2})$

Step 1.1.2

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

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

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

Step 1.2

Pull terms out from under the radical.

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

Step 1.3

Multiply $5$ by $5$ .

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

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

Step 2

Subtract $6 \sqrt{2}$ from $25 \sqrt{2}$ .

$\sqrt{10} (19 \sqrt{2})$

Step 3

Multiply $\sqrt{10} (19 \sqrt{2})$ .

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Step 3.1

Combine using the product rule for radicals.

$19 \sqrt{10 \cdot 2}$

Step 3.2

Multiply $10$ by $2$ .

$19 \sqrt{20}$

$19 \sqrt{20}$

Step 4

Rewrite $20$ as $2^{2} \cdot 5$ .

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Step 4.1

Factor $4$ out of $20$ .

$19 \sqrt{4 (5)}$

Step 4.2

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

$19 \sqrt{2^{2} \cdot 5}$

$19 \sqrt{2^{2} \cdot 5}$

Step 5

Pull terms out from under the radical.

$19 (2 \sqrt{5})$

Step 6

Multiply $2$ by $19$ .

$38 \sqrt{5}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$38 \sqrt{5}$

Decimal Form:

$84.97058314 \dots$

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