Curriculum
Course: Mathematics — Second Preparatory
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Curriculum

Mathematics — Second Preparatory

Unit 1: Real Numbers

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Unit 2: Algebra

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Unit 3: Geometry

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Unit 4: Statistics

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Text lesson

Operations on Real Numbers

Mathematics — Second Preparatory

Operations on Real Numbers

Worked examples

Worked examples

Comparison aspectMain ideaKeywords
Example 1Simplify √12 + √27Simplify
Solution√12 = 2√3 and √27 = 3√3. So √12 + √27 = 2√3 + 3√3 = 5√3
Example 2Find the value of (2 + √3)(2 − √3)Findvalue
SolutionUse the difference of two squares: 22 − (√3)2 = 4 − 3 = 1.differencesquares
Example 3
  • Remove the root from the denominator of 2 ÷ (√5 − 1)
  • then find its approximate value
Removerootdenominatorthen
SolutionMultiply the numerator and the denominator by (√5 + 1): 2(√5 + 1) ÷ ((√5)2 − 12) = 2(√5 + 1) ÷ 4 = (√5 + 1) ÷ 2. Its approximate value is 1.618.Multiplynumeratordenominatorapproximate
Example 4Simplify (√8 + √18) ÷ √2Simplify
Solution
  • √8 = 2√2 and √18 = 3√2
  • so the expression becomes (2√2 + 3√2) ÷ √2 = 5√2 ÷ √2 = 5
expressionbecomes
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