Simplification · Question 14 · Hard
Find the value of 1/(3 − √8) − 1/(√8 − √7) + 1/(√7 − √6) − 1/(√6 − √5) + 1/(√5 − 2).
- 0
- 1
- 2√2
- 5
Answer and explanation
Answer: D. 5
Explanation: Rationalising, 1/(√a − √b) = √a + √b when a − b = 1. The sum becomes (3 + √8) − (√8 + √7) + (√7 + √6) − (√6 + √5) + (√5 + 2) = 3 + 2 = 5.
Previous: Simplify: (0.75^3 − 0.25^3) ÷ (0.75^2 + 0.75 × 0.25 + 0.25^2) · Next: If x + 1/x = 5, find the value of x^3 + 1/x^3.
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