Surds Cambridge IGCSE Mathematics (9–1) revision
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In plain words
√2 is 1.41421356… and never ends or repeats. Rather than round it, mathematicians leave it as √2 and work with it exactly. A root left like this is called a surd, and surds follow a few simple rules.
Three things to know
- √a × √b = √(ab), and √a ÷ √b = √(a ÷ b).
- To simplify, find a square number that divides in: √50 = √25 × √2 = 5√2.
- To rationalise a denominator, multiply the top and the bottom by the surd: 1/√3 = √3/3. And (a + √b)(a − √b) = a² − b, which has no surd in it.
Worked example
Simplify √12 + √27.
- √12 = √4 × √3 = 2√3.
- √27 = √9 × √3 = 3√3.
- 2√3 + 3√3 = 5√3.
Tips and tricks
- You can add surds only when the number under the root is the same, like collecting like terms. √2 + √3 is not √5.
- Look for the biggest square factor: 4, 9, 16, 25, 36…
It lands in your notebook with its questions as flashcards.
Surds: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
What is √18 in its simplest form?
√9 × √2.
What is √5 × √5?
A square root times itself gives the number.
What is √8 + √2?
√8 = 2√2, and 2√2 + √2 = 3√2.
What is 1/√5 with a rational denominator?
Multiply top and bottom by √5.
What is √20 ÷ √5?
√(20 ÷ 5) = √4.
Quiz
5 questions
Tap an answer and you’ll see straight away whether it’s right, and why.
Worksheet
4 questions, 8 marks. Write your answers on paper, then check them.
Surds
Cambridge IGCSE Mathematics (9–1) 0980 · 8 marks · papermunch.org
Name ______________________________ Date ______________
Simplify √72.[2]
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6√2. √36 × √2.
Work out √3 × √12.[2]
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6. √36.
Rationalise the denominator of 6/√2.[2]
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3√2. 6√2 ÷ 2.
Expand and simplify (2 + √3)(2 − √3).[2]
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1. 4 − 3.
Answers: Surds
- 1. 6√2. √36 × √2.
- 2. 6. √36.
- 3. 3√2. 6√2 ÷ 2.
- 4. 1. 4 − 3.