Skill: Add and subtract like radicals

Like radicals have the same radical part after simplifying. To add or subtract them, combine only their coefficients and keep the radical part unchanged.

For example, simplify:

$$2\sqrt{12}+3\sqrt{27}-\sqrt{3}$$

Step 1: Simplify each radical.

Factor out perfect squares:

$$\sqrt{12}=\sqrt{4\cdot3}=2\sqrt3$$ $$\sqrt{27}=\sqrt{9\cdot3}=3\sqrt3$$

Substitute these into the expression:

$$2(2\sqrt3)+3(3\sqrt3)-\sqrt3$$

Step 2: Multiply the coefficients.

$$4\sqrt3+9\sqrt3-\sqrt3$$

Remember that $\sqrt3$ has an invisible coefficient of $1$:

$$4\sqrt3+9\sqrt3-1\sqrt3$$

Step 3: Combine the coefficients.

$$4+9-1=12$$

Therefore,

$$\boxed{12\sqrt3}$$

Do not add the radicands. For example, $\sqrt2+\sqrt3$ cannot be combined because the radicals are unlike.