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ITMC 2018 Grade 8 National Preliminary set01 Question 27

ITMC · ITMC 2018 Grade 8 National Preliminary set01

Question 27

Answer-format rule: round a non-integer answer to the nearest integer. If the calculated answer has more than five digits, give its last five digits.

Let $d_1,d_2,\ldots,d_n$ be an increasing sequence of different integers, each a factor of 2500. How many numbers in $\sqrt{d_1},\sqrt{d_2},\ldots,\sqrt{d_n}$ are rational?