Add and Subtract Like Radicals

Add and Subtract Like Radicals

When radicals are like radicals, they have the same radical part. That means the numbers under the radical sign, and the type of radical, match. In that case, you can combine them just like like terms.

1) Identify the like radicals

Look for radicals with the same index and the same radicand. For example, (3\sqrt{5}) and (-2\sqrt{5}) are like radicals, but (\sqrt{5}) and (\sqrt{7}) are not.

2) Add or subtract the coefficients

Keep the radical part unchanged and combine only the numbers in front.

• (3\sqrt{5} + 2\sqrt{5} = 5\sqrt{5})
• (7\sqrt{2} - 4\sqrt{2} = 3\sqrt{2})

If there is no visible coefficient, the coefficient is 1.

3) Simplify the result

If possible, reduce any numerical coefficients or simplify the radical itself before finishing. If the radicals are already in simplest form and are like, your answer should usually stay in radical form.

Check your work

Make sure:

• only like radicals were combined,
• the radical part stayed the same,
• the final answer is simplified.

If a problem includes unlike radicals, do not combine them. First simplify each radical if needed, then combine only those that match.