The square root of 448 is approximately 21.166. To understand how we arrive at this, we can break it down further.
First, we can simplify the number 448. It can be factored into its prime components:
- 448 = 16 × 28
- 16 = 4 × 4 = 2^4
- 28 = 4 × 7 = 2^2 × 7
So, when we completely factor 448, we have:
448 = 2^4 × (2^2 × 7) = 2^6 × 7
Now, we can find the square root:
√448 = √(2^6 × 7) = √(2^6) × √7 = 2^3 × √7 = 8√7
Since √7 is approximately 2.645751, we can further estimate:
8 × 2.645751 ≈ 21.166
This gives us the approximate square root of 448, which is 21.166.