The square root of 108 in radical form is expressed as 6√3.
To understand how we arrive at this, we can start by simplifying the square root of 108.
First, we can factor 108 into its prime factors:
- 108 = 2 × 2 × 3 × 3 × 3
- 108 = 2² × 3³
Next, we can use the property of square roots that states
√(a × b) = √a × √b. Applying this to our factors:
- √108 = √(2² × 3³)
- √108 = √(2²) × √(3³)
- √108 = 2 × √(3 × 3 × 3)
- √108 = 2 × 3 × √3
- √108 = 6√3
Therefore, the square root of 108 in radical form is 6√3.