What is the Square Root of 192?

The square root of 192 is approximately 13.8564. To understand this better, let’s break it down.

The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, 13.8564 multiplied by itself equals 192.

Here’s a step-by-step explanation:

1. First, find the prime factors of 192. The prime factorization of 192 is 2 × 2 × 2 × 2 × 2 × 2 × 3, or 2⁶ × 3.
2. Next, pair the prime factors. Since 2⁶ can be written as (2³)², we have (2³)² × 3.
3. Take the square root of each pair. The square root of (2³)² is 2³, which is 8.
4. Now, multiply this by the square root of the remaining unpaired factor, which is √3. So, 8 × √3 ≈ 8 × 1.732 = 13.8564.

Therefore, the square root of 192 is approximately 13.8564.