To simplify the square root of 148, we start by finding the prime factorization of 148. The number 148 can be divided by 2, which is a prime number:
- 148 ÷ 2 = 74
- 74 ÷ 2 = 37
Now we have:
148 = 2 × 2 × 37 = 2² × 37
Next, we apply the square root to each factor:
√148 = √(2² × 37)
Using the property of square roots, we can separate the factors:
√148 = √(2²) × √37
Since the square root of 2² is 2, we simplify further:
√148 = 2 × √37
So, the simplified form of the square root of 148 is:
2√37