Simplify square root of 128

Problem

√(,128)

Solution

1. Identify the largest perfect square factor of the radicand 128

2. Factor the number 128 into the product of 64 and 2

√(,128)=√(,64⋅2)

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

√(,64⋅2)=√(,64)⋅√(,2)

4. Evaluate the square root of the perfect square 64

√(,64)=8

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

8⋅√(,2)=8√(,2)

Final Answer

√(,128)=8√(,2)

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