what is the smallest number i have to multiply with 315 to get a perfect square?
315 = 3^2 * 5 * 7
so if you multiply by 5*7 = 35 you get 3^2 5^2 7^2
To find the smallest number you have to multiply with 315 to get a perfect square, we need to break down 315 into its prime factors and find the missing factors that will make it a perfect square.
The prime factorization of 315 is: 3 × 3 × 5 × 7
To make it a perfect square, we need to have an even exponent for each prime factor. We can see that the exponent of 3 is odd, so we need to multiply 315 by another 3 to make the exponent of 3 even.
Therefore, the smallest number you need to multiply with 315 to get a perfect square is 3.
315 × 3 = 945, which is a perfect square because its prime factorization is 3 × 3 × 3 × 5 × 7 × 7.
To find the smallest number you need to multiply with 315 to get a perfect square, we can begin by finding the prime factorization of 315.
The prime factorization of 315 is:
315 = 3 x 3 x 5 x 7
To make the number a perfect square, we need to have an equal number of each prime factor.
Looking at the prime factorization, we see that there are two 3's, one 5, and one 7. To make it a perfect square, we need to have two of each prime factor.
To achieve this, we can multiply 315 by the remaining prime factors needed.
We multiply 315 by 3 x 5 x 7:
315 x 3 x 5 x 7 = 315 x 105 = 33075
33075 is the smallest number you have to multiply with 315 to get a perfect square.