What is the smallest positive integer by which 180 should be multiplied to obtain a perfect square? Thank you
5 * 180 = 900 = A perfect square.
5 x 180 = 900
The answer is 5.
To find the smallest positive integer by which 180 should be multiplied to obtain a perfect square, we need to find the prime factorization of 180 and determine the highest power of each prime factor.
The prime factorization of 180 is: 2 * 2 * 3 * 3 * 5
To obtain a perfect square, we need to have an even power for each prime factor.
Since there is only one factor of 5, we need to multiply 180 by 5 to obtain an even power of 5.
So, the smallest positive integer by which 180 should be multiplied to obtain a perfect square is 5.
Therefore, 180 * 5 = 900, which is a perfect square.
To find the smallest positive integer by which 180 should be multiplied to obtain a perfect square, we need to find the prime factorization of 180 and check the exponent of each prime factor.
The prime factorization of 180 is 2^2 * 3^2 * 5^1.
For 180 to be a perfect square, the exponents of all prime factors in its prime factorization should be even.
The exponent of 2 is 2, which is already even.
The exponent of 3 is 2, which is already even.
The exponent of 5 is 1, which is odd.
To make the exponent of 5 even, we need to multiply 180 by 5^1, which is 5.
Therefore, 180 needs to be multiplied by 5 to obtain a perfect square.
The smallest positive integer by which 180 should be multiplied to obtain a perfect square is 5.