Square Root Addition

How to Add Square Roots

You can only add square roots when they are like radicals — meaning they have the same number under the square root sign.

Rule: Like radicals can be added

Example: 3√2 + 5√2 = (3+5)√2 = 8√2

Example: 4√5 + 2√5 = 6√5

Unlike radicals — simplify first

Sometimes radicals that look different can be simplified to the same form. Example: √8 + √2 = 2√2 + √2 = 3√2 (because √8 = √(4×2) = 2√2)

Cannot be added

√2 ≈ 1.414 and √3 ≈ 1.732, so √2 + √3 ≈ 3.146. But √5 ≈ 2.236. They are not equal.