The 5 digit number 5abc9 is the square of an integer where a, b, and c represent a missing digit. If all five digits are different, what is the five-digit number?

54289.

Explanation:

The square root will be a 3 digit number and as the last digit of the given number is 9 the last digit of the square root will be a 3 or a 7.

√50000 = 223.6 and the √60000 = 244 so we try the following numbers:

243^2 = 59049 NO

237^2 = 56169. NO

233^2 = 54289 YES.

54289 = 233^2

You know the last digit of the squared number is 3 or 7, so just try numbers ending with those from 220 to 250