Find the square root of 324 using factor method
To find the square root of 324 using the factor method, we need to consider the prime factors of 324.
The factors of 324 are:
1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, and 324.
The prime factorization of 324 is:
2^2 × 3^4.
Now, let's simplify the prime factorization by taking out pairs of identical factors.
2^2 × 3^4 = (2 × 2) × (3 × 3 × 3 × 3) = 2 × 2 × 3 × 3 × 3 × 3 = (2 × 3)^2 × 3^2.
Therefore, the square root of 324 is √(2 × 3)^2 × 3^2 = 2 × 3 × 3 = 18.
To find the square root of 324 using the factor method, we need to find the factors of 324.
The factors of 324 are:
1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324
Now, let's pair up these factors starting from the smallest and largest numbers:
1 and 324
2 and 162
3 and 108
4 and 81
6 and 54
9 and 36
12 and 27
Since we are looking for the square root, we are looking for a pair where the two numbers are equal. In this case, we have a pair of 18 and 18.
Therefore, the square root of 324 is 18.