Can you solve this easy math problem?

Question

Both the square root and the cube root of 1 are integers. The next such number is 64. What is the next number whose square root and cube are both integers? How many numbers like this exist from 1 to 1000?

Answer 1

The key is looking at cubes which are under 1000, only 1^3, 4^3, 9^3, which are 1, 64, and 729, which are cubes of squares. Even if increasing the range to 100,000. You only add 16^3, 25^3, and 36^3 which are 4,096, 15,625, and 46,656. Cubes add up very quickly..


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