. Using prime factor method, find the square root of 3600
The correct answer and explanation is:
Correct Answer:
The square root of 3600 using the prime factor method is 60.
Explanation:
To find the square root of 3600 using the prime factorization method, begin by breaking down 3600 into its prime factors.
Start by dividing by the smallest prime numbers:
3600 ÷ 2 = 1800
1800 ÷ 2 = 900
900 ÷ 2 = 450
450 ÷ 2 = 225 (2 no longer divides evenly)
Now move to the next prime number, which is 3:
225 ÷ 3 = 75
75 ÷ 3 = 25 (3 no longer divides evenly)
Next prime number is 5:
25 ÷ 5 = 5
5 ÷ 5 = 1
Now list the prime factorization:
3600 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5
Group the factors into pairs:
= (2 × 2) × (3 × 3) × (5 × 5) × (2 × 2)
= (2²) × (2²) × (3²) × (5²)
To find the square root, take one number from each pair:
√3600 = √[(2²) × (2²) × (3²) × (5²)]
= 2 × 2 × 3 × 5
= 60
The square root of a number is a value that, when multiplied by itself, gives the original number. By using prime factorization, one simplifies the process by expressing the number as a product of primes and then identifying perfect squares. Grouping prime factors into pairs and taking one from each helps find the exact square root. This method is useful for perfect square numbers and gives a clear view of their factor structure. Hence, the square root of 3600 is 60.