1. The number 25{+6}{+4}x 64{+2}{+5}is the square of a positive integer N. Find the sum of the digits in the decimal representation of N?

Solution

1) 14

Explanation: The given number can be written as N{+2}= (5{+2}){+6}{+4}x (2{+6}){+2}{+5}and so N = 5{+6}{+4}x (2{+3}){+2}{+5}= (5x2){+6}{+4}X 2048 = 10{+6}{+4}x 2048 , Which is 2048 followed by 64 zeros. Since zeros do not contribute to the sum, the sum of the digits of the given number is 2+4+8 = 14.