Evaluate square root of 512

Problem

√(,512)

Solution

1. Identify the number under the radical and look for perfect square factors.

2. Factor the number 512 into a product of a perfect square and another integer.

512=256⋅2

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

√(,512)=√(,256⋅2)

√(,512)=√(,256)⋅√(,2)

4. Simplify the square root of the perfect square. Since 16=256 then √(,256)=16

√(,512)=16√(,2)

Final Answer

√(,512)=16√(,2)

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