Simplify the Radical Expression -3 cube root of -3+2 cube root of 162+3 cube root of 81

$- 3 \sqrt[3]{- 3} + 2 \sqrt[3]{162} + 3 \sqrt[3]{81}$

Step 1

Simplify each term.

Rewrite $- 3$ as ${(- 1)}^{3} \cdot 3$ .

Rewrite $- 3$ as $- 1 (3)$ .

$- 3 \sqrt[3]{- 1 (3)} + 2 \sqrt[3]{162} + 3 \sqrt[3]{81}$

Rewrite $- 1$ as ${(- 1)}^{3}$ .

$- 3 \sqrt[3]{{(- 1)}^{3} \cdot 3} + 2 \sqrt[3]{162} + 3 \sqrt[3]{81}$

Pull terms out from under the radical.

$- 3 (- 1 \sqrt[3]{3}) + 2 \sqrt[3]{162} + 3 \sqrt[3]{81}$

Rewrite $- 1 \sqrt[3]{3}$ as $- \sqrt[3]{3}$ .

$- 3 (- \sqrt[3]{3}) + 2 \sqrt[3]{162} + 3 \sqrt[3]{81}$

Multiply $- 1$ by $- 3$ .

$3 \sqrt[3]{3} + 2 \sqrt[3]{162} + 3 \sqrt[3]{81}$

Rewrite $162$ as $3^{3} \cdot 6$ .

Factor $27$ out of $162$ .

$3 \sqrt[3]{3} + 2 \sqrt[3]{27 (6)} + 3 \sqrt[3]{81}$

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

$3 \sqrt[3]{3} + 2 \sqrt[3]{3^{3} \cdot 6} + 3 \sqrt[3]{81}$

Pull terms out from under the radical.

$3 \sqrt[3]{3} + 2 (3 \sqrt[3]{6}) + 3 \sqrt[3]{81}$

Multiply $3$ by $2$ .

$3 \sqrt[3]{3} + 6 \sqrt[3]{6} + 3 \sqrt[3]{81}$

Rewrite $81$ as $3^{3} \cdot 3$ .

Factor $27$ out of $81$ .

$3 \sqrt[3]{3} + 6 \sqrt[3]{6} + 3 \sqrt[3]{27 (3)}$

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

$3 \sqrt[3]{3} + 6 \sqrt[3]{6} + 3 \sqrt[3]{3^{3} \cdot 3}$

Pull terms out from under the radical.

$3 \sqrt[3]{3} + 6 \sqrt[3]{6} + 3 (3 \sqrt[3]{3})$

Multiply $3$ by $3$ .

$3 \sqrt[3]{3} + 6 \sqrt[3]{6} + 9 \sqrt[3]{3}$

Step 2

Add $3 \sqrt[3]{3}$ and $9 \sqrt[3]{3}$ .

$12 \sqrt[3]{3} + 6 \sqrt[3]{6}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$12 \sqrt[3]{3} + 6 \sqrt[3]{6}$

Decimal Form:

$28.20971840 \dots$