Evaluate -2 square root of 75

Problem

−2√(,75)

Solution

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

2. Factor the number inside the square root into a product of a perfect square and another number.

75=25⋅3

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

−2√(,25⋅3)=−2⋅√(,25)⋅√(,3)

4. Evaluate the square root of the perfect square.

√(,25)=5

5. Multiply the coefficients outside the radical.

−2⋅5⋅√(,3)=−10√(,3)

Final Answer

−2√(,75)=−10√(,3)

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