Take Least Common Multiplier (commonly referred as LCM) of 169.

Start dividing 169 by 2, 3, 4, 5, ... Carry on dividing until 169 is divisible completely. By completely, I mean to say that the end result must be a whole number and not a decimal fraction or you can say that we are looking for a divisor. (For example; 6 is completely divisible by 2 as 2x3 = 6. Here both 2 and 3 are divisors of 6)

Well while searching for a divisor for 169, you discard 2, 3, 4, .., 11, 12 on your way through and finally come across 13 which is the only number that divides 169 completely or a divisor of 169. Now 13 multiplied by which whole number results in 169? Your answer again is 13. I.e. 13x13 = 169.

In order to find square root, one has to multiply two same numbers. Hence in this case, it is obvious that 13x13 = √169. Thus, square root of 169 comes out to be 13.

Start dividing 169 by 2, 3, 4, 5, ... Carry on dividing until 169 is divisible completely. By completely, I mean to say that the end result must be a whole number and not a decimal fraction or you can say that we are looking for a divisor. (For example; 6 is completely divisible by 2 as 2x3 = 6. Here both 2 and 3 are divisors of 6)

Well while searching for a divisor for 169, you discard 2, 3, 4, .., 11, 12 on your way through and finally come across 13 which is the only number that divides 169 completely or a divisor of 169. Now 13 multiplied by which whole number results in 169? Your answer again is 13. I.e. 13x13 = 169.

In order to find square root, one has to multiply two same numbers. Hence in this case, it is obvious that 13x13 = √169. Thus, square root of 169 comes out to be 13.