Evaluate square root of 175

Problem

√(,175)

Solution

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

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

175=25⋅7

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

√(,175)=√(,25⋅7)

√(,175)=√(,25)⋅√(,7)

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

√(,25)=5

5. Combine the results to write the expression in simplest radical form.

√(,175)=5√(,7)

Final Answer

√(,175)=5√(,7)

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