Evaluate square root of 75

Problem

√(,75)

Solution

1. Identify the number inside the radical and look for its prime factors.

2. Factor the number 75 into a product of its prime factors.

75=3⋅25

75=3⋅5⋅5

3. Group the factors into pairs of perfect squares.

75=3⋅5

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

√(,75)=√(,5⋅3)

√(,75)=√(,5)⋅√(,3)

5. Simplify the square root of the perfect square.

√(,5)=5

√(,75)=5√(,3)

Final Answer

√(,75)=5√(,3)

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