Simplify square root of 125

Problem

√(,125)

Solution

1. Identify the radicand and look for perfect square factors.

2. Factor the number 125 into a product of a perfect square and another number.

125=25⋅5

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

√(,25⋅5)=√(,25)⋅√(,5)

4. Simplify the square root of the perfect square.

√(,25)=5

5. Combine the results to reach the simplest radical form.

5⋅√(,5)=5√(,5)

Final Answer

√(,125)=5√(,5)

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