How-to · Updated October 2, 2026
How do you add and subtract radicals?
Direct answer
Simplify each radical, then combine only like radicals — the same index and the same radicand. 5√28 − 7√7 = 3√7, because 5√28 = 10√7 and 10 − 7 = 3.
Worked examples
| Expression | Simplest form |
|---|---|
| 5√28 − 7√7 | 3√7 |
| 2√12 + 3√27 | 13√3 |
| √8 × √24 | 8√3 |
| √2 + ∛4 | √2 + ∛4 |
Why 5√28 becomes 10√7
- Simplify each radical first: 5√28 = 10√7; 7√7 is already simplest.
- Both are like radicals (same index and radicand: √7). Add or subtract the coefficients: 10 − 7 = 3.
- Result: 5√28 − 7√7 = 3√7.
Limits
- Coefficients add, and the radicand stays. 10√7 − 7√7 is 3√7.
- Unlike radicals stay as a sum. √2 + ∛4 has no single-radical form.
- √a × √b = √(ab) when a and b are not both negative. Two negative radicands need i first, because i × i = −1.
Use the calculator
Simplifying one root first: how to write a square root in simplest radical form. Combine two terms in the simplest radical form calculator.