Calculate the square root of 500

Problem

√(,500)

Solution

1. Identify the number inside the radical and look for the largest perfect square factor.

2. Factor the number 500 into a product of a perfect square and another integer.

√(,500)=√(,100⋅5)

3. Apply the product property of radicals, which states that √(,a⋅b)=√(,a)⋅√(,b)

√(,100⋅5)=√(,100)⋅√(,5)

4. Simplify the square root of the perfect square.

√(,100)=10

5. Combine the results to find the simplified radical form.

10⋅√(,5)=10√(,5)

Final Answer

√(,500)=10√(,5)

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