Simplify square root of 125n

Problem

√(,125*n)

Solution

1. Identify the radicand and look for perfect square factors of the numerical coefficient.

2. Factor the number 125 into a product of its prime factors or a perfect square and another factor.

125=25⋅5

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

√(,125*n)=√(,25⋅5*n)

4. Simplify the square root of the perfect square factor.

√(,25)=5

5. Combine the simplified parts back into a single expression.

5√(,5*n)

Final Answer

√(,125*n)=5√(,5*n)

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