If √(12 - 2√35) + √(8 + 2√15) = √a + √b, where a and b are positive integers,…
2020
If √(12 - 2√35) + √(8 + 2√15) = √a + √b, where a and b are positive integers, then the value of b - a is closest to:
- A.
5
- B.
3
- C.
2
- D.
4
Attempted by 2 students.
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Correct answer: D
sqrt(12 - 2sqrt35) = sqrt7 - sqrt5 because 7 + 5 = 12 and 2sqrt(7 x 5) = 2sqrt35.
sqrt(8 + 2sqrt15) = sqrt5 + sqrt3 because 5 + 3 = 8 and 2sqrt(5 x 3) = 2sqrt15.
Adding them gives sqrt7 + sqrt3. Therefore, b - a = 7 - 3 = 4.