Simplify square root of 250

Problem

√(,250)

Solution

1. Identify the largest perfect square factor of the radicand 250

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

√(,250)=√(,25⋅10)

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

√(,25⋅10)=√(,25)⋅√(,10)

4. Evaluate the square root of the perfect square.

√(,25)=5

5. Combine the terms to reach the simplest form.

5⋅√(,10)=5√(,10)

Final Answer

√(,250)=5√(,10)

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