Adding/Subtracting Radicals

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

You can add or subtract radicals only if they have the same index and radicand (the number under the root). For example, $$3\sqrt{2} + 5\sqrt{2} = 8\sqrt{2}$$ .

The index of a radical indicates the degree of the root. For example, in $$\sqrt{a}$$ , the index is 2 (square root). In $$\sqrt[3]{a}$$ , the index is 3 (cube root).

Simplifying a radical means to express it in its simplest form, removing any perfect square factors from under the radical sign.

$$\sqrt{7}$$ .

$$-6\sqrt{7}$$ .

0.

$$6\sqrt{5}$$ .

Combine like terms by adding or subtracting the coefficients of the radicals that have the same radicand. For example, $$3\sqrt{2} + 2\sqrt{2} = 5\sqrt{2}$$ .

$$2\sqrt{5}$$ .