When adding or subtracting "like" radicals (kak\sqrt{a} with the same aa), combine the coefficients. It often helps to simplify each radical first. Products and quotients are usually reduced to a single radical using ab\sqrt{ab} and a/b\sqrt{a/b}.
ma±na=(m±n)am\sqrt{a}\pm n\sqrt{a}=(m\pm n)\sqrt{a}
a⋅b=ab\sqrt{a}\cdot\sqrt{b}=\sqrt{ab} for a,b≥0a,b\ge0
Sometimes expand brackets first, then combine like terms
Sample simplifications.
Simplify the radical
27+12\sqrt{27}+\sqrt{12}
=53=5\sqrt{3}
=33+23=3\sqrt{3}+2\sqrt{3}=53=5\sqrt{3}
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