The Solution

It is not easy to find out if a number is a perfect cube.  To find out which of the numbers 9896830520 to 9896830529 is a perfect cube square would indeed be tough.

Take 9896830520. Group the digits into threes as 9 896 830 520. The cube root of 9 being above 2 but less than 3, the first digit of the cube root of 9896830520 would be 2.

The cube root of 9896 being above 21 but less than 22 (not an easy task!), we find that the first two digits of the cube root of 9896830520 would be 21.

Struggling thus, we find that 9896830520 is not a perfect cube. The last digit has to be 3 because 9896830523 is a perfect cube.

(Luckily, it was the last digit that got washed out. The task would have indeed been much tougher if it was one of the earlier digits.)

Perhaps you would prefer a shorter method? Try the Smart Scholars method.

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