# Exam Questions on Surds

These lessons, with videos, examples and step-by-step solutions, help GCSE Maths students learn about surds by working through some examination questions.

Surds Exam questions

Examples:

1. (a) Write √45 in the form a √5, where a is an integer.
(b) Express 2(3 + √5)(2 + √5) in the form b + c√5, where b and c are integers.
2. (a) Expand and simplify (4 + √3)(4 - √3).
(b) Express 26/(4+√3) in the form a + b√3, where a and b are integers.
3. (a) Express √108 in the form a√3, where a in an integer.
(b) Express (2 - √3)2 in the form b + c√3 where b and c integers to be found.
4. Simplify (3 + √5)(3 - √5)
5. Simplify (5 - √3)/(2 + √3) giving your answer in the form a + b√3, where a and b are integers.

How to do Surds GCSE A/A* Maths revision?
(simplifying, rationalising)

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 