Final answer:
The question asked to simplify √147, which can be factored into 3 x 7 x 7. By applying square root properties, we find that the correct answer is Option 3: 7√3, as the square root of a perfect square, 72, is simply 7, and the square root of 3 remains under the radical.
Step-by-step explanation:
The question involves simplifying the square root of 147. To simplify the expression √147, we need to factor 147 into its prime factors. We find that 147 = 3 x 7 x 7. By utilizing the properties of square roots, we split this into √(3 x 72). The square root of a perfect square, which is 72 in this case, is just the base of the square, so √72 = 7. Therefore, we get 7√3, which is the product of the square root of a non-perfect square and an integer. Hence, the correct answer is Option 3: 7√3.