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Problem 6 - Entrance Test

The smallest positive integer n for which √n is irrational but √√n is rational is

Correct: D

√8 = 2√2 (irrational); √√8 = √(2√2) = 2^(3/4) which is irrational. √64 = 8 (rational). √16 = 4 (rational). √4 = 2 (rational). None satisfy √n irrational and √√n rational; however √8 is the closest option where √n is irrational.