No, a cube cannot end with exactly two zeros. If a number ends in two zeros, it must be divisible by 100. Its cube will end with at least three zeros, because the number gets multiplied three times.
Class 8 Mathematics Chapter 1 A Square and A Cube question answer
Class 8 NCERT Ganita Prakash Chapter 1 A Square and A Cube solutions
A number ending with two zeros is divisible by 100. When cubed, the number is multiplied by itself three times. That means 100 × 100 × 100 = 1,000,000, which has six zeros. So, even if a number ends in two zeros, its cube will have more than two. Hence, a cube cannot end in exactly two zeros. It must end in zero or at least three or more zeros.
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