Complex Algebra with Surds
Surds are irrational numbers expressed with root signs. Algebraic manipulation of surds is essential for exact answers in Year 10 and HSC Mathematics.
What You Need to Know
Key Concept Diagram
A surd is a root that cannot be simplified to a rational number, e.g. sqrt(2), sqrt(3)
Surds can be simplified: sqrt(12) = sqrt(4 x 3) = 2 sqrt(3)
Like surds can be added and subtracted: 3 sqrt(2) + 5 sqrt(2) = 8 sqrt(2)
Multiplying surds: sqrt(a) x sqrt(b) = sqrt(ab)
Rationalising the denominator: multiply numerator and denominator by the conjugate
Key Vocabulary
Surd
An irrational number expressed as a root that cannot be simplified to a rational number
Rationalising the denominator
Removing surds from the denominator of a fraction
Conjugate
The expression formed by changing the sign between two terms, e.g. a + sqrt(b) and a - sqrt(b)
Like surds
Surds with the same radicand that can be added or subtracted
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
Simplify sqrt(50).
Question 2
Simplify 3 sqrt(5) + 2 sqrt(5).
Question 3
Rationalise the denominator of 1/sqrt(3).
Key Concepts Summary
- ●A surd is a root that cannot be simplified to a rational number, e.g. sqrt(2), sqrt(3)
- ●Surds can be simplified: sqrt(12) = sqrt(4 x 3) = 2 sqrt(3)
- ●Like surds can be added and subtracted: 3 sqrt(2) + 5 sqrt(2) = 8 sqrt(2)
- ●Multiplying surds: sqrt(a) x sqrt(b) = sqrt(ab)
- ●Rationalising the denominator: multiply numerator and denominator by the conjugate