Algebra Examples

$\sqrt[3]{16} + 7 \sqrt[3]{2} - \sqrt[3]{54}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Rewrite $16$ as $2^{3} \cdot 2$ .

Tap for more steps...

Step 1.1.1

Factor $8$ out of $16$ .

$\sqrt[3]{8 (2)} + 7 \sqrt[3]{2} - \sqrt[3]{54}$

Step 1.1.2

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

$\sqrt[3]{2^{3} \cdot 2} + 7 \sqrt[3]{2} - \sqrt[3]{54}$

Step 1.2

Pull terms out from under the radical.

$2 \sqrt[3]{2} + 7 \sqrt[3]{2} - \sqrt[3]{54}$

Step 1.3

Rewrite $54$ as $3^{3} \cdot 2$ .

Tap for more steps...

Step 1.3.1

Factor $27$ out of $54$ .

$2 \sqrt[3]{2} + 7 \sqrt[3]{2} - \sqrt[3]{27 (2)}$

Step 1.3.2

Rewrite $27$ as $3^{3}$ .

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

Step 1.4

Pull terms out from under the radical.

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

Step 1.5

Multiply $3$ by $- 1$ .

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

Step 2

Simplify by adding terms.

Tap for more steps...

Step 2.1

Add $2 \sqrt[3]{2}$ and $7 \sqrt[3]{2}$ .

$9 \sqrt[3]{2} - 3 \sqrt[3]{2}$

Step 2.2

Subtract $3 \sqrt[3]{2}$ from $9 \sqrt[3]{2}$ .

$6 \sqrt[3]{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$6 \sqrt[3]{2}$

Decimal Form:

$7.55952629 \dots$