Evaluate 2 cube root of 6- sixth root of 6+3 cube root of 6-3 sixth root of 384

$2 \sqrt[3]{6} - \sqrt[6]{6} + 3 \sqrt[3]{6} - 3 \sqrt[6]{384}$

Step 1

Simplify each term.

Rewrite $384$ as $2^{6} \cdot 6$ .

Factor $64$ out of $384$ .

$2 \sqrt[3]{6} - \sqrt[6]{6} + 3 \sqrt[3]{6} - 3 \sqrt[6]{64 (6)}$

Rewrite $64$ as $2^{6}$ .

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

Pull terms out from under the radical.

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

Multiply $2$ by $- 3$ .

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

Step 2

Simplify by adding terms.

Add $2 \sqrt[3]{6}$ and $3 \sqrt[3]{6}$ .

$5 \sqrt[3]{6} - \sqrt[6]{6} - 6 \sqrt[6]{6}$

Subtract $6 \sqrt[6]{6}$ from $- \sqrt[6]{6}$ .

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$- 0.35044011 \dots$