What a surd is, taking square factors out of a root, and adding and subtracting like surds.
What you will learn
- Tell a surd from a whole number
- Simplify a surd like √48
- Add and subtract surds
- Compare surds without a calculator
What a surd is
A surd is a square root that is not a whole number: √2, √5, √12.
√9 = 3 is not a surd. Surds let you give exact answers: √2 = 1.41421356... never ends, but √2 is exact.
The key rule:
√(ab) = √a × √b
The rest of this lesson and its 7 practice questions are locked.
In this lesson
- What a surd is
- Take out the biggest square factor
- Like surds add like letters
- Try it: Check a simplification numerically
7 practice questions, marked as you go; about 20 minutes in all.
Key terms
Surd, Exact
In this unit: Surds
Exact answers with square roots: simplifying, multiplying and expanding, rationalising denominators, and surds in Pythagoras and quadratics. Higher tier.