Trigonometry Examples

$\sqrt{50} - 3 \sqrt{8} + \sqrt{32}$

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 $50$ .

$\sqrt{25 (2)} - 3 \sqrt{8} + \sqrt{32}$

Step 1.1.2

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

$\sqrt{5^{2} \cdot 2} - 3 \sqrt{8} + \sqrt{32}$

$\sqrt{5^{2} \cdot 2} - 3 \sqrt{8} + \sqrt{32}$

Step 1.2

Pull terms out from under the radical.

$5 \sqrt{2} - 3 \sqrt{8} + \sqrt{32}$

Step 1.3

Rewrite $8$ as $2^{2} \cdot 2$ .

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Step 1.3.1

Factor $4$ out of $8$ .

$5 \sqrt{2} - 3 \sqrt{4 (2)} + \sqrt{32}$

Step 1.3.2

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

$5 \sqrt{2} - 3 \sqrt{2^{2} \cdot 2} + \sqrt{32}$

$5 \sqrt{2} - 3 \sqrt{2^{2} \cdot 2} + \sqrt{32}$

Step 1.4

Pull terms out from under the radical.

$5 \sqrt{2} - 3 (2 \sqrt{2}) + \sqrt{32}$

Step 1.5

Multiply $2$ by $- 3$ .

$5 \sqrt{2} - 6 \sqrt{2} + \sqrt{32}$

Step 1.6

Rewrite $32$ as $4^{2} \cdot 2$ .

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Step 1.6.1

Factor $16$ out of $32$ .

$5 \sqrt{2} - 6 \sqrt{2} + \sqrt{16 (2)}$

Step 1.6.2

Rewrite $16$ as $4^{2}$ .

$5 \sqrt{2} - 6 \sqrt{2} + \sqrt{4^{2} \cdot 2}$

$5 \sqrt{2} - 6 \sqrt{2} + \sqrt{4^{2} \cdot 2}$

Step 1.7

Pull terms out from under the radical.

$5 \sqrt{2} - 6 \sqrt{2} + 4 \sqrt{2}$

$5 \sqrt{2} - 6 \sqrt{2} + 4 \sqrt{2}$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $6 \sqrt{2}$ from $5 \sqrt{2}$ .

$- \sqrt{2} + 4 \sqrt{2}$

Step 2.2

Add $- \sqrt{2}$ and $4 \sqrt{2}$ .

$3 \sqrt{2}$

$3 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{2}$

Decimal Form:

$4.24264068 \dots$

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