Final answer:
To find the square root of a number using the prime factorization method, you factorize the number into its prime factors and simplify the square root based on the exponent of each prime factor.
Step-by-step explanation:
a. To find the square root of 8, we can factorize 8 into its prime factors: 8 = 2 × 2 × 2. Therefore, √√8 = √(2 × 2 × 2) = 2√2.
b. To find the square root of 625, we can factorize 625 into its prime factors: 625 = 5 × 5 × 5 × 5. Therefore, √625 = 5 × 5 = 25.
c. To find the square root of 144, we can factorize 144 into its prime factors: 144 = 2 × 2 × 2 × 2 × 3 × 3. Therefore, √144 = 2 × 2 × 3 = 12.
Learn more about Solving square roots using prime factorization