Simplify square root of 175

Problem

√(,175)

Solution

1. Identify the largest perfect square factor of the number inside the radical.

2. Factor the number 175 into a product of its largest perfect square factor and another integer.

√(,175)=√(,25⋅7)

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

√(,25⋅7)=√(,25)⋅√(,7)

4. Simplify the square root of the perfect square.

√(,25)⋅√(,7)=5√(,7)

Final Answer

√(,175)=5√(,7)

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