Adding and Subtracting Radicals

A radical is an expression that includes a root, such as a square root (√) or cube root (∛). For example, √4 is a radical.

To simplify a radical, factor the number under the root into its prime factors and look for pairs. For example, √50 = √(25*2) = 5√2.

$$7\text{√}6$$ .

Yes, you can add them because they have the same radical part. The result is $$6\text{√}3$$ .

$$4\text{√}8$$ .

$$12\text{√}5 + 4\text{√}5$$ can be added because they have the same radical.

$$-5\text{√}2$$ .

Combining like radicals means adding or subtracting radicals that have the same index and radicand. For example, $$2\text{√}3 + 3\text{√}3 = 5\text{√}3$$ .

$$6\text{√}2$$ .

$$40\text{√}2$$ .