Surds & Irrational Numbers
Surds are square roots (or other roots) that cannot be simplified to rational numbers. They arise frequently in geometry and algebra.
What You Need to Know
Key Concept Diagram
A surd is an irrational number written as a root, e.g. √2, √3, √5
Simplify surds by finding perfect square factors: √12 = 2√3
Multiply surds: √a × √b = √(ab)
Rationalise the denominator by multiplying by the surd
Key Vocabulary
Surd
An irrational number expressed as a root that cannot be simplified to a rational number
Rationalise
To eliminate surds from the denominator of a fraction
Perfect square
A number whose square root is a whole number (e.g. 4, 9, 16, 25)
Irrational number
A number that cannot be expressed as a fraction of two integers
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
Which of the following is a surd?
Question 2
Simplify √48
Question 3
What is √5 × √5?
Key Concepts Summary
- ●A surd is an irrational number written as a root, e.g. √2, √3, √5
- ●Simplify surds by finding perfect square factors: √12 = 2√3
- ●Multiply surds: √a × √b = √(ab)
- ●Rationalise the denominator by multiplying by the surd