what should be multiplied to number 103875 to make it a perfect square
I don't know the SMALLEST number that should be multiplied to 103875 to make it a perfect square. But the most obvious answer here is to multiply it by 103875 (the number itself), since
103875 * 103875 = 103875 ^ 2
any square contains at least a PAIR of equal factors
e.g 1600 = 5x5 x 8x8
so ...
103875 = 25x4155
= 25 x 5 x 831
= 25 x 5 x 3 x 277 , and 277 is prime
so to make pairs, we need a 5, a 3, and a 277
5(3)(277) = 4155
so if 103875 is multiplied by 4155 the result is a perfect square, and it is the smallest multiplier
check:
103875(4155) = 431600625
and √431600625 = 20775
To determine what number should be multiplied by 103875 to make it a perfect square, we need to find the factors of 103875 and check if any of them can be multiplied by another factor to obtain a perfect square.
First, let's find the prime factorization of 103875:
103875 = 3 * 5^3 * 139
Since a perfect square has all its prime factors appearing in pairs, we need to check if any of the prime factors can be paired up. In this case, we have a single prime factor of 139, which does not have a pair.
To make 103875 a perfect square, we need to multiply it by a number that includes the missing factor(s) so that all the factors appear in pairs. In this case, we multiply 103875 by 139 to obtain a perfect square.
Multiplying 103875 by 139:
103875 * 139 = 14425875
Therefore, you need to multiply 103875 by 139 to make it a perfect square.