Simplify numerical surds

A question is this type if and only if it asks to simplify a numerical expression involving square roots into the form k√n, such as √45 + √20 or √180 - √80.

15 questions · Easy -1.5

1.02b Surds: manipulation and rationalising denominators
Sort by: Default | Easiest first | Hardest first
Edexcel C1 2010 June Q1
2 marks Easy -1.8
  1. Write
$$\sqrt { } ( 75 ) - \sqrt { } ( 27 )$$ in the form \(k \sqrt { } x\), where \(k\) and \(x\) are integers.
Edexcel C1 2013 June Q2
4 marks Easy -1.8
Express \(\frac { 15 } { \sqrt { 3 } } - \sqrt { 27 }\) in the form \(k \sqrt { } 3\), where \(k\) is an integer.
OCR C1 2005 January Q1
6 marks Easy -1.8
1
  1. Express \(11 ^ { - 2 }\) as a fraction.
  2. Evaluate \(100 ^ { \frac { 3 } { 2 } }\).
  3. Express \(\sqrt { 50 } + \frac { 6 } { \sqrt { 3 } }\) in the form \(a \sqrt { } 2 + b \sqrt { } 3\), where \(a\) and \(b\) are integers.
OCR C1 2007 June Q3
5 marks Easy -1.8
3 Simplify the following, expressing each answer in the form \(a \sqrt { 5 }\).
  1. \(3 \sqrt { 10 } \times \sqrt { 2 }\)
  2. \(\sqrt { 500 } + \sqrt { 125 }\)
OCR C1 2008 June Q3
4 marks Easy -1.8
3 Express each of the following in the form \(k \sqrt { 2 }\), where \(k\) is an integer:
  1. \(\sqrt { 200 }\),
  2. \(\frac { 12 } { \sqrt { 2 } }\),
  3. \(5 \sqrt { 8 } - 3 \sqrt { 2 }\).
OCR C1 2009 January Q1
3 marks Easy -1.2
1 Express \(\sqrt { 45 } + \frac { 20 } { \sqrt { 5 } }\) in the form \(k \sqrt { 5 }\), where \(k\) is an integer.
OCR C1 2011 June Q5
6 marks Easy -1.3
5
  1. Express \(\sqrt { 300 } - \sqrt { 48 }\) in the form \(k \sqrt { 3 }\), where \(k\) is an integer.
  2. Express \(\frac { 15 + \sqrt { 40 } } { \sqrt { 5 } }\) in the form \(a \sqrt { 5 } + b \sqrt { 2 }\), where \(a\) and \(b\) are integers.
AQA C1 2006 January Q1
4 marks Easy -1.8
1
  1. Simplify \(( \sqrt { 5 } + 2 ) ( \sqrt { 5 } - 2 )\).
  2. Express \(\sqrt { 8 } + \sqrt { 18 }\) in the form \(n \sqrt { 2 }\), where \(n\) is an integer.
Edexcel C1 Q2
4 marks Easy -1.8
2. Express \(\sqrt { 22.5 }\) in the form \(k \sqrt { 10 }\).
AQA C1 2008 June Q2
6 marks Easy -1.3
2 It is given that \(x = \sqrt { 3 }\) and \(y = \sqrt { 12 }\).
Find, in the simplest form, the value of:
  1. \(x y\);
  2. \(\frac { y } { x }\);
  3. \(( x + y ) ^ { 2 }\).
Pre-U Pre-U 9794/1 2016 June Q2
2 marks Easy -1.8
2 Without using a calculator, simplify the following, giving each answer in the form \(a \sqrt { 5 }\) where \(a\) is an integer. Show all your working.
  1. \(4 \sqrt { 10 } \times \sqrt { 2 }\)
  2. \(\sqrt { 500 } + \sqrt { 125 }\)
OCR C1 2013 June Q1
4 marks Easy -1.3
Express each of the following in the form \(a\sqrt{5}\), where \(a\) is an integer.
  1. \(4\sqrt{15} \times \sqrt{3}\) [2]
  2. \(\frac{20}{\sqrt{5}}\) [1]
  3. \(5^{\frac{3}{2}}\) [1]
OCR C1 2014 June Q2
5 marks Easy -1.3
Express each of the following in the form \(k\sqrt{3}\), where \(k\) is an integer.
  1. \(\frac{6}{\sqrt{3}}\) [1]
  2. \(10\sqrt{3} - 6\sqrt{27}\) [2]
  3. \(3^{\frac{3}{2}}\) [2]
Edexcel C1 Q1
3 marks Easy -1.2
Express \(\sqrt{50} + 3\sqrt{8}\) in the form \(k\sqrt{2}\). [3]
OCR C1 Q2
4 marks Easy -1.2
Express \(\sqrt{22.5}\) in the form \(k\sqrt{10}\). [4]