Operations with Radicals

$$-4\sqrt{2}$$  

$$2\sqrt{2}$$  

$$-6\sqrt{6}$$  

$$-6\sqrt{10}$$  

$$6\sqrt{2}-6$$  

$$3\sqrt{2}+3$$  

$$6-\sqrt{3}$$  

$$\sqrt{3}-\sqrt{2}$$  

$$17\sqrt{2}$$  

$$0$$  

$$9$$  

$$9\sqrt{2}$$  

$$0$$

$$2\sqrt{5}$$

$$\sqrt{15}$$  

$$-2\sqrt{15}$$  

$$3\sqrt{2}-6\sqrt{5}$$

$$-5\sqrt{3}$$

$$\sqrt{2}-6\sqrt{5}$$

$$\sqrt{4}-6\sqrt{5}$$

4√12

6√3

4√3

4√2

$$13\sqrt[]{x}$$  

$$6x\sqrt[]{x}$$  

$$x\sqrt[]{x^{12}}$$  

$$x^{6\sqrt[]{x}}$$  

It is incorrect because $$\sqrt[]{64}\ne\sqrt[]{4\cdot16}$$  

Removing the 4 from under the radical in the second step is incorrect or invalid.

The work shown above is correct; however,   $$2\sqrt[]{16}$$  may be simplified further.

The work shown above is correct, and $$2\sqrt[]{16}$$   may not be simplified further.