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Edexcel IGCSE Math A Higher 1.4.HB Manipulate surds

Edexcel IGCSE Math A Higher 1.4.HB Manipulate surds
Edexcel IGCSE Math A syllabusMath A 4MA1First assessment 2018

Practise manipulating surds by expanding brackets, simplifying radicals and rationalising denominators without a calculator.

How this is tested

  • rationalise denominators using a conjugate and simplify into forms
  • expand and collect surd terms to prove identities or solve equations involving √2 or √3
  • use surd manipulation in contexts

Question 17(b)

[Maximum number: 3]

Given that 8m+49m−9m=km8 \sqrt{m}+\sqrt{49 m}-\sqrt{9 m}=k \sqrt{m} where k is an integer and m is a prime number,

Show that 5−181−2\frac{5-\sqrt{18}}{1-\sqrt{2}} can be written in the form a+b2a+b \sqrt{2}
where a and b are integers.
Show each stage of your working clearly.