Evaluate square root of 192

Problem

√(,192)

Solution

1. Identify the largest perfect square factor of the radicand 192

2. Factor the number 192 into a product of a perfect square and another integer.

192=64⋅3

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

√(,192)=√(,64⋅3)

√(,192)=√(,64)⋅√(,3)

4. Simplify the square root of the perfect square 64

√(,64)=8

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

8⋅√(,3)=8√(,3)

Final Answer

√(,192)=8√(,3)

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