Simplify square root of 75

Problem

√(,75)

Solution

1. Identify the largest perfect square factor of the radicand 75

2. Factor the number 75 into the product of that perfect square and another integer.

√(,75)=√(,25⋅3)

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

√(,25⋅3)=√(,25)⋅√(,3)

4. Simplify the square root of the perfect square 25

√(,25)⋅√(,3)=5√(,3)

Final Answer

√(,75)=5√(,3)

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