Expand and simplify surd expressions

A question is this type if and only if it asks to expand brackets containing surds and simplify, such as (3 + √5)(3 - √5) or (5 - √8)(1 + √2), typically resulting in the form a + b√c.

31 questions · Easy -1.2

1.02b Surds: manipulation and rationalising denominators
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OCR MEI C1 2006 June Q7
5 marks Moderate -0.8
  1. Simplify \(6\sqrt{2} \times 5\sqrt{3} - \sqrt{24}\). [2]
  2. Express \((2 - 3\sqrt{5})^2\) in the form \(a + b\sqrt{5}\), where \(a\) and \(b\) are integers. [3]
OCR MEI C1 2009 June Q8
5 marks Easy -1.3
  1. Simplify \(\frac{\sqrt{48}}{2\sqrt{27}}\). [2]
  2. Expand and simplify \((5 - 3\sqrt{2})^2\). [3]
Edexcel C1 Q1
4 marks Easy -1.3
  1. Express \(\frac{18}{\sqrt{3}}\) in the form \(k\sqrt{3}\). [2]
  2. Express \((1 - \sqrt{3})(4 - 2\sqrt{3})\) in the form \(a + b\sqrt{3}\) where \(a\) and \(b\) are integers. [2]
Edexcel C1 Q3
6 marks Moderate -0.5
\includegraphics{figure_1} Figure 1 shows the rectangles \(ABCD\) and \(EFGH\) which are similar. Given that \(AB = (3 - \sqrt{5})\) cm, \(AD = \sqrt{5}\) cm and \(EF = (1 + \sqrt{5})\) cm, find the length \(EH\) in cm, giving your answer in the form \(a + b\sqrt{5}\) where \(a\) and \(b\) are integers. [6]
OCR MEI C1 Q3
4 marks Easy -1.2
You are given that \(n\), \(n + 1\) and \(n + 2\) are three consecutive integers.
  1. Expand and simplify \(n^2 + (n + 1)^2 + (n + 2)^2\). [2]
  2. For what values of \(n\) will the sum of the squares of these three consecutive integers be an even number? Give a reason for your answer. [2]
OCR MEI C1 Q12
5 marks Moderate -0.8
  1. Simplify \(6\sqrt{2} \times 5\sqrt{3} \times \sqrt{24}\). [2]
  2. Express \((2 - 3\sqrt{5})^2\) in the form \(a + b\sqrt{5}\), where \(a\) and \(b\) are integers. [3]