To add or subtract expressions containing radicals, combine terms that have the same number inside the radical.
Rules for Addition and Subtraction
a√m + b√m = (a+b)√m
Terms with different numbers inside the radicals cannot be calculated together as they are.
📘 Example ①
Calculate 3√2 + 5√2.
Solution: 3√2 + 5√2 = (3+5)√2 = 8√2
Calculate 3√2 + 5√2.
Solution: 3√2 + 5√2 = (3+5)√2 = 8√2
📘 Example ②
Calculate √12 + √3.
Solution: Since √12 = 2√3, 2√3 + √3 = 3√3
Calculate √12 + √3.
Solution: Since √12 = 2√3, 2√3 + √3 = 3√3
💡 Key Points
- First simplify the expressions inside the radicals (√12 = 2√3, for example), then calculate
- Only terms with the same number inside the radical can be added or subtracted (the same idea as like terms in algebraic expressions)
- √2 and √3 are different terms and cannot be combined
Practice Problems
- Calculate 4√5 − √5.
- Calculate √8 + √2.
Answers and Explanations
- Answer: 4√5 − √5 = 3√5
- Answer: Since √8 = 2√2, 2√2 + √2 = 3√2