Evaluate square root of 108

Problem

√(,108)

Solution

1. Identify the number inside the radical and look for its prime factors.

2. Factor the number 108 into its prime components.

108=2×54

108=2×2×27

108=2×2×3×9

108=2×3×3

3. Group the factors into perfect squares to simplify the radical.

√(,108)=√(,2×3×3)

4. Apply the product property of radicals √(,a×b)=√(,a)×√(,b) to separate the perfect squares.

√(,108)=√(,2)×√(,3)×√(,3)

5. Simplify by taking the square root of the perfect squares.

√(,108)=2×3×√(,3)

√(,108)=6√(,3)

Final Answer

√(,108)=6√(,3)

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