Simplify 2 square root of 18+3 cube root of 27-4 cube root of 16

$2 \sqrt{18} + 3 \sqrt[3]{27} - 4 \sqrt[3]{16}$

Rewrite $18$ as $3^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$2 \sqrt{9 (2)} + 3 \sqrt[3]{27} - 4 \sqrt[3]{16}$

Rewrite $9$ as $3^{2}$ .

$2 \sqrt{3^{2} \cdot 2} + 3 \sqrt[3]{27} - 4 \sqrt[3]{16}$

Pull terms out from under the radical.

$2 (3 \sqrt{2}) + 3 \sqrt[3]{27} - 4 \sqrt[3]{16}$

Multiply $3$ by $2$ .

$6 \sqrt{2} + 3 \sqrt[3]{27} - 4 \sqrt[3]{16}$

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

$6 \sqrt{2} + 3 \sqrt[3]{3^{3}} - 4 \sqrt[3]{16}$

Pull terms out from under the radical, assuming real numbers.

$6 \sqrt{2} + 3 \cdot 3 - 4 \sqrt[3]{16}$

Multiply $3$ by $3$ .

$6 \sqrt{2} + 9 - 4 \sqrt[3]{16}$

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

Factor $8$ out of $16$ .

$6 \sqrt{2} + 9 - 4 \sqrt[3]{8 (2)}$

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

$6 \sqrt{2} + 9 - 4 \sqrt[3]{2^{3} \cdot 2}$

Pull terms out from under the radical.

$6 \sqrt{2} + 9 - 4 (2 \sqrt[3]{2})$

Multiply $2$ by $- 4$ .

$6 \sqrt{2} + 9 - 8 \sqrt[3]{2}$

The result can be shown in multiple forms.

Exact Form:

$6 \sqrt{2} + 9 - 8 \sqrt[3]{2}$

Decimal Form:

$7.40591297 \dots$