Basic Math Examples

$\sqrt[3]{20} - \sqrt{80} + 6 \sqrt{40}$

Step 1

Rewrite $80$ as $4^{2} \cdot 5$ .

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Step 1.1

Factor $16$ out of $80$ .

$\sqrt[3]{20} - \sqrt{16 (5)} + 6 \sqrt{40}$

Step 1.2

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

$\sqrt[3]{20} - \sqrt{4^{2} \cdot 5} + 6 \sqrt{40}$

Step 2

Pull terms out from under the radical.

$\sqrt[3]{20} - (4 \sqrt{5}) + 6 \sqrt{40}$

Step 3

Multiply $4$ by $- 1$ .

$\sqrt[3]{20} - 4 \sqrt{5} + 6 \sqrt{40}$

Step 4

Rewrite $40$ as $2^{2} \cdot 10$ .

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Step 4.1

Factor $4$ out of $40$ .

$\sqrt[3]{20} - 4 \sqrt{5} + 6 \sqrt{4 (10)}$

Step 4.2

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

$\sqrt[3]{20} - 4 \sqrt{5} + 6 \sqrt{2^{2} \cdot 10}$

Step 5

Pull terms out from under the radical.

$\sqrt[3]{20} - 4 \sqrt{5} + 6 (2 \sqrt{10})$

Step 6

Multiply $2$ by $6$ .

$\sqrt[3]{20} - 4 \sqrt{5} + 12 \sqrt{10}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\sqrt[3]{20} - 4 \sqrt{5} + 12 \sqrt{10}$

Decimal Form:

$31.71747762 \dots$