Simplify square root of 108

Problem

√(,108)

Solution

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

2. Factor the number 108 into a product of a perfect square and another integer.

108=36⋅3

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

√(,36⋅3)=√(,36)⋅√(,3)

4. Simplify the square root of the perfect square.

√(,36)=6

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

6⋅√(,3)=6√(,3)

Final Answer

√(,108)=6√(,3)

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