Evaluate: [1 / (sqrt(9) - sqrt(8))] - [1 / (sqrt(8) - sqrt(7))] + [1 / (sqrt(7) - sqrt(6))] - [1 / (sqrt(6) - sqrt(5))] + [1 / (sqrt(5) - sqrt(4))].

Answer and explanation

Correct answer: D. 5

  1. Step 1: Rationalize each term: 1/(√n - √(n-1)) = √n + √(n-1).
  2. Step 2: Expression becomes: (√9 + √8) - (√8 + √7) + (√7 + √6) - (√6 + √5) + (√5 + √4).
  3. Step 3: Telescoping cancellation: √9 + √4 = 3 + 2 = 5.

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Evaluate: [1 / (sqrt(9) - sqrt(8))]… | CAT Powers and roots