12/10/2025
To find the square root of 600, we'll break it down step by step.
1. *Understand the concept:* The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, we need to find a number that, when multiplied by itself, equals 600.
2. *Prime factorization:* Let's break down 600 into its prime factors:
600 = 2 × 2 × 2 × 3 × 5 × 5
600 = 2^3 × 3 × 5^2
3. *Simplify the square root:* Now, let's simplify the square root of 600 using its prime factors:
√600 = √(2^3 × 3 × 5^2)
√600 = √(2^2 × 2 × 3 × 5^2)
√600 = 2 × 5 × √(2 × 3)
√600 = 10√6
4. *Calculate the square root of 6:* To find the approximate value of √6, we can use a calculator or estimate it:
√6 ≈ 2.449
5. *Calculate the final result:* Now, multiply 10 by the square root of 6:
√600 ≈ 10 × 2.449
√600 ≈ 24.49
Therefore, the square root of 600 is approximately *24.49*.
