What is the smallest number that 7800 must be multiplied by to give a square number?

Answer 1

Oh, dude, let me break it down for you. So, 7800 is 2^3 * 3 * 5^2 * 13. To make it a square number, each prime factor needs to appear an even number of times. So, the smallest number it must be multiplied by is 2 * 5 * 13, which is 130. Easy peasy lemon squeezy!

Answer 2

To find the smallest number that 7800 must be multiplied by to give a square number, we need to factorize 7800 into its prime factors. The prime factorization of 7800 is 2^3 * 3 * 5^2 * 13. To make it a square number, we need to pair up the prime factors so that each exponent is even. Therefore, the smallest number it must be multiplied by is 5 to make it a square number, resulting in 7800 * 5 = 39000, which is a square number (200^2).

Answer 3

Well, isn't that a happy little question! To find the smallest number that 7800 must be multiplied by to give a square number, we need to break down 7800 into its prime factors. Once we have those, we can pair them up to form perfect squares. By doing this, we can see that the smallest number 7800 must be multiplied by to give a square number is 3, because when we pair up all the prime factors, we have every factor in pairs except for one factor of 3. And just like that, we've painted a beautiful solution!