Algebra Examples

$\sqrt[3]{750} + \sqrt[3]{2058} - \sqrt[3]{48}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $750$ as $5^{3} \cdot 6$ .

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Step 1.1.1

Factor $125$ out of $750$ .

$\sqrt[3]{125 (6)} + \sqrt[3]{2058} - \sqrt[3]{48}$

Step 1.1.2

Rewrite $125$ as $5^{3}$ .

$\sqrt[3]{5^{3} \cdot 6} + \sqrt[3]{2058} - \sqrt[3]{48}$

Step 1.2

Pull terms out from under the radical.

$5 \sqrt[3]{6} + \sqrt[3]{2058} - \sqrt[3]{48}$

Step 1.3

Rewrite $2058$ as $7^{3} \cdot 6$ .

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Step 1.3.1

Factor $343$ out of $2058$ .

$5 \sqrt[3]{6} + \sqrt[3]{343 (6)} - \sqrt[3]{48}$

Step 1.3.2

Rewrite $343$ as $7^{3}$ .

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

Step 1.4

Pull terms out from under the radical.

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

Step 1.5

Rewrite $48$ as $2^{3} \cdot 6$ .

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Step 1.5.1

Factor $8$ out of $48$ .

$5 \sqrt[3]{6} + 7 \sqrt[3]{6} - \sqrt[3]{8 (6)}$

Step 1.5.2

Rewrite $8$ as $2^{3}$ .

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

Step 1.6

Pull terms out from under the radical.

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

Step 1.7

Multiply $2$ by $- 1$ .

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

Step 2

Add $5 \sqrt[3]{6}$ and $7 \sqrt[3]{6}$ .

$12 \sqrt[3]{6} - 2 \sqrt[3]{6}$

Step 3

Subtract $2 \sqrt[3]{6}$ from $12 \sqrt[3]{6}$ .

$10 \sqrt[3]{6}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$10 \sqrt[3]{6}$

Decimal Form:

$18.17120592 \dots$