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"between" implies two numbers: the question gives only one of them.
The square root is between 5 and 6.
The square roots of 82 are -9.055 and 9.055. So two consecutive whole numbers that lie between the square roots of 82 are any consecutive numbers from the set {-9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
Every sixth number will be a multiple of 6, so you need at least six consecutive numbers to guarantee that one of them will be divisible by 6.
The numbers are 5, 6, and 7.