Example 16 - Simplify the following expressions: - Class 9 - Simplifying real numbers

  1. Chapter 1 Class 9 Number Systems
  2. Serial order wise
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Example 16 Simplify the following expressions: (5 + √7) (2 + √5) (5 + √7) (2 + √5) = 5 (2 + √5) + √7 (2 + √5) = 5 × 2 + 5 × √5 + √7 × 2+ √5 × √7 = 10 + 5√5 + 2√7+ √(5" ×" 7) = 10 + 5√5 + 2√7 + √35 Example 16 Simplify the following expressions: (ii) (5 + √5) (5 - √5) (5 + √5) (5 - √5) We know that, (a + b) (a-b) = a2 – b2 Putting a = 5, b = √5 = 52 – (√5)2 = 25 – 5 = 20 Example 16 Simplify the following expressions: (iii) (√3 + √7)2 (√3 + √7)2 We know that (a + b)2= a2 + b2 + 2ab where a = √3 , b = √7 = (√3)2 +(√7)2 + 2√3 √7 = 3 + 7 + 2√(3×7) = 3 + 7 + 2√21 = 10 + 2 √21 Example 16 Simplify the following expressions: (iv) (√11 – √7) (√11 + √7) (√11 – √7) (√11 + √7) We know that, (a + b) (a-b) = a2 – b2 Putting a = √11, b = √7 = (√11)2 – (√7)2 = 11 – 7 = 4

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