Adding and subtracting surds Flashcards
(7 cards)
What is a surd?
A surd is a square root (or other root) that cannot be simplified to a whole number.
Examples: √2, √3, √5 = surds (irrational); √4 = 2 (not a surd — it’s rational!)
When can you add or subtract surds?
Only when the radical part is the same — like terms only!
✅ √3 + 2√3 = 3√3; ❌ √3 + √2 = leave it like that, they aren’t compatible
How do you simplify surds?
Break the surd into square factors:
Example: √50 = √(25 × 2) = √25 × √2 = 5√2
Why simplify surds before adding or subtracting?
So you can see if they’re like terms!
Example: √50 + √8 👉 Simplify first: 5√2 + 2√2 = 7√2
Simplify: √18 + √8
Break ‘em down:
√18 = √(9×2) = 3√2
√8 = √(4×2) = 2√2
Add like terms: 3√2 + 2√2 = 5√2
What do I do if surds aren’t like terms?
If they can’t be simplified to the same radical, leave them.
Example: √3 + √7 = can’t simplify, so keep it like that.
What are common mistakes when adding/subtracting surds?
❌ Trying to add unlike surds (e.g. √5 + √7 ≠ √12)
❌ Adding the numbers inside the root (e.g. √2 + √2 ≠ √4 — it’s 2√2)
✅ Always simplify before adding/subtracting!