How do you simplify the square root of 5000?

To simplify the square root of 5000, you can break it down into its prime factors and then simplify the square root expression:

Find the prime factorization of 5000:
5000 = 2 * 2 * 2 * 5 * 5 * 5 * 5 = 2^3 * 5^4

Now, simplify the square root expression:
√5000 = √(2^3 * 5^4)

Use the properties of square roots to simplify further:
√(2^3 * 5^4) = √(2^2 * 2 * 5^2 * 5^2) = √(2^2) * √(2 * 5^2 * 5^2)

Simplify each part of the expression:
√(2^2) = 2
√(2 * 5^2 * 5^2) = √2 * 5^2 = 10 * 5 = 50

Multiply the simplified parts together:
2 * 50 = 100

So, √5000 simplifies to 100.