Simplify square root of 32

Problem

√(,32)

Solution

1. Identify the largest perfect square factor of the number inside the radical.

2. Factor the number 32 into the product of its largest perfect square factor and another integer.

√(,32)=√(,16⋅2)

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

√(,16⋅2)=√(,16)⋅√(,2)

4. Simplify the square root of the perfect square.

√(,16)⋅√(,2)=4√(,2)

Final Answer

√(,32)=4√(,2)

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