go step by step to reduce the radical. square root of 72
To simplify the square root of 72, we need to factorize 72 into its prime factors.
1. Start by finding the prime factorization of 72:
72 = 2 x 36
= 2 x 2 x 18
= 2 x 2 x 2 x 9
= 2 x 2 x 2 x 3 x 3
2. Now, we can rewrite the square root of 72 as the square root of (2 x 2 x 2 x 3 x 3).
3. Next, we can simplify the square root by taking out the pairs of identical numbers:
√(2 x 2 x 2 x 3 x 3) = 2 x 3 x √2
4. Therefore, the simplified form of the square root of 72 is 6√2.