Evaluate square root of 128

Problem

√(,128)

Solution

1. Identify the number under the radical and look for its largest perfect square factor.

2. Factor the number 128 into a product of a perfect square and another integer.

√(,128)=√(,64⋅2)

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

√(,64⋅2)=√(,64)⋅√(,2)

4. Simplify the square root of the perfect square.

√(,64)=8

5. Combine the results to find the final simplified form.

8⋅√(,2)=8√(,2)

Final Answer

√(,128)=8√(,2)

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