A surd is a root that cannot be simplified to a whole number, such as √2 or √12. To simplify a surd, find the largest square number that is a factor: √12 = √4 × √3 = 2√3.
Like surds can be added just like like terms: √24 + √96 = 2√6 + 4√6 = 6√6. You cannot add √2 and √3 together, just as you cannot add x and y. Multiplying works too: √a × √b = √(ab).
Worked example
Simplify √75 − √12
- √75 = 5√3 and √12 = 2√3.
- 5√3 − 2√3 = 3√3.
Answer:3√3
Key words
- surd
- an irrational root, such as √2
- simplify
- take out square factors
- exact
- left as a surd, not a rounded decimal
Practise this
New questions every time.
Common Core-referenced: HSN-RN.A.2