Find the square root of 1225using factorisation method
To find the square root of 1225 using the factorization method, we need to express 1225 as the product of its prime factors.
The prime factorization of 1225 is: 5 * 5 * 7 * 7.
Now, we can take the square root of each factor separately:
sqrt(5 * 5 * 7 * 7) = sqrt(5) * sqrt(5) * sqrt(7) * sqrt(7)
Next, we simplify the square roots:
sqrt(5) * sqrt(5) = 5
sqrt(7) * sqrt(7) = 7
Therefore, the square root of 1225 is:
sqrt(1225) = 5 * 7
Thus, the square root of 1225 is 35.
To find the square root of 1225 using the factorization method, we need to factorize 1225 into its prime factors and then find the square root.
Step 1: Prime Factorization of 1225
To factorize 1225, we can start by dividing it by the smallest prime number, which is 2. If a number is divisible by 2, we divide it by 2. If not, we move on to the next prime number, which is 3, and continue this process until we reach a prime number that is greater than the square root of the given number.
1225 ÷ 2 = 612.5 (not divisible by 2)
1225 ÷ 3 = 408.3 (not divisible by 3)
1225 ÷ 4 = 306.25 (not divisible by 4)
1225 ÷ 5 = 245 (divisible by 5)
We can divide 1225 by 5, which gives us 245.
245 ÷ 5 = 49 (divisible by 5)
We can divide 245 by 5 again, which gives us 49.
49 is a prime number, so we stop here.
So, the prime factorization of 1225 is 5 × 5 × 7 × 7.
Step 2: Find the Square Root
Now that we have the prime factorization of 1225, we can find the square root.
sqrt(1225) = sqrt(5 × 5 × 7 × 7)
Using the property of square roots, we can separate the numbers inside the square root:
sqrt(5 × 5 × 7 × 7) = sqrt(5) × sqrt(5) × sqrt(7) × sqrt(7)
Simplifying further:
sqrt(5) × sqrt(5) × sqrt(7) × sqrt(7) = 5 × 7
Therefore, the square root of 1225 is 5 × 7 = 35.
Hence, the square root of 1225 using the factorization method is 35.