Answer: 8
Step-by-step explanation: If we are trying to take the square root of 64, one way to evaluate or simplify the square root is to use prime factorization.
First, we can draw two branches coming down from 64 and we can put 2 on the left and 32 on the right since 2 × 32 = 64.
Next, we can draw two branches coming down from 32 and we can put a 2 on the left and 16 on the right since 2 × 16 = 32.
Next, we can draw two branches coming down from 16 and we can put a 2 on the left and a 8 on the right since 2 × 8 = 16.
Then, we can draw two branches coming down from 8 and put a 2 on the left and a 4 on the right since 2 × 4 = 8.
Finally, we can draw two more branches coming down from 4 and we can put a 2 both on the left and right side. Now, we are done factoring.
It's important to understand that we can rewrite this as the square root of the prime factorization which is 2 × 2 × 2 × 2 × 2 × 2.
When you are taking the square root, you can take the square root of pairs of numbers. This means that I can take the square root of 2 × 2, of 2 × 2, and of 2 × 2 because those are pairs. So, we can rewrite this as 2 × 2 × 2 or 8.
Whenever you need to find square root, you can break it up into its prime factorization and then group pairs that you can take the square root of.