4MA1/2H Jan 2022, Question 17: Surds
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 3 marks
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The question, in short
Show that √12/(√3 + 2) can be written as a + √b with a and b integers.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 3 marks
- 1Multiply the top and the bottom by √3 − 2.
- 2Bottom: (√3 + 2)(√3 − 2) = 3 − 4 = −1
- 3Top: √12 × (√3 − 2) = √36 − 2√12 = 6 − 2√12
- 4√12 = 2√3, so the top is 6 − 4√3
- 5Dividing 6 − 4√3 by −1 gives 4√3 − 6
- 64√3 = √48, so the expression is −6 + √48
Answer−6 + √48
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