Trigonometry Examples

$\sqrt[5]{3} - \sqrt{98} + \sqrt{48} + \sqrt[6]{2}$

Step 1

Rewrite $98$ as $7^{2} \cdot 2$ .

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Step 1.1

Factor $49$ out of $98$ .

$\sqrt[5]{3} - \sqrt{49 (2)} + \sqrt{48} + \sqrt[6]{2}$

Step 1.2

Rewrite $49$ as $7^{2}$ .

$\sqrt[5]{3} - \sqrt{7^{2} \cdot 2} + \sqrt{48} + \sqrt[6]{2}$

Step 2

Pull terms out from under the radical.

$\sqrt[5]{3} - (7 \sqrt{2}) + \sqrt{48} + \sqrt[6]{2}$

Step 3

Multiply $7$ by $- 1$ .

$\sqrt[5]{3} - 7 \sqrt{2} + \sqrt{48} + \sqrt[6]{2}$

Step 4

Rewrite $48$ as $4^{2} \cdot 3$ .

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Step 4.1

Factor $16$ out of $48$ .

$\sqrt[5]{3} - 7 \sqrt{2} + \sqrt{16 (3)} + \sqrt[6]{2}$

Step 4.2

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

$\sqrt[5]{3} - 7 \sqrt{2} + \sqrt{4^{2} \cdot 3} + \sqrt[6]{2}$

Step 5

Pull terms out from under the radical.

$\sqrt[5]{3} - 7 \sqrt{2} + 4 \sqrt{3} + \sqrt[6]{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\sqrt[5]{3} - 7 \sqrt{2} + 4 \sqrt{3} + \sqrt[6]{2}$

Decimal Form:

$- 0.60309871 \dots$