**Solving 4√1250**

To solve the expression 4√1250, we need to simplify the square root of 1250 first.

**Simplifying √1250:**

To simplify the square root of 1250, we can break it down into its prime factors.

- The prime factorization of 1250 is 2 * 5 * 5 * 5 * 5.
- We can pair the prime factors into pairs of two, where each pair consists of two identical factors.
- In this case, we have one pair of 5s, so we can take it out of the square root.
- The remaining factors are 2 and 5, which cannot be paired further.
- Therefore, we can simplify the square root of 1250 as √(2 * 5 * 5 * 5) = 5√(2 * 5).

**Simplifying 4√1250:**

Now that we have simplified the square root of 1250, we can substitute it back into the original expression 4√1250.

4√1250 = 4 * 5√(2 * 5)

- We can simplify this expression further by multiplying the coefficients outside the square root.
- 4 * 5 equals 20, so the expression becomes 20√(2 * 5).

**Final Simplification:**

To summarize, the simplified form of 4√1250 is 20√(2 * 5).

**Answer:**
20√(2 * 5)

Note: Remember to use the proper mathematical symbols and formatting when writing the final answer.