Is 1225 a perfect square check it by prime factorization method?

Is 1225 a perfect square check it by prime factorization method?

The square root is the number (integer) which when multiplied by itself results in the original number. The 2nd root of 1225 is +35 or -35. This shows that 1225 is a perfect square.

What are the multiples of 1225?

The first 5 multiples of 1225 are 1225, 2450, 3675, 4900, 6125. The sum of the first 5 multiples of 1225 is 18375 and the average of the first 5 multiples of 1225 is 3675. Multiples of 1225: 1225, 2450, 3675, 4900, 6125, 7350, 8575, 9800, 11025, 12250 and so on.

How do you find the square root of 289 using prime factorization?

To find the square root of 289: We can use prime factorization method to obtain one number from each pair of the same numbers and multiply them. The factorization of 289 is 17 × 17 which consists of 1 pair of the same number, 17. Thus, the square root of 289 is √(17 × 17) = 17 itself.

What’s the prime factorization of 4900?

So, the prime factorization of 4900 can be written as 22 × 52 × 72 where 2, 5, 7 are prime.

What is the prime factorization of 7056?

Since, the prime factors of 7056 are 2, 3, 7. Therefore, the product of prime factors = 2 × 3 × 7 = 42.

How are the prime factors of 1225 calculated?

The same step can be applied 1 more time and the resultant value will be 49. Continuing, the number 49 is divisible by prime number 7 and the result after division will be 7. The result 7 cannot be divided any further as it is a prime number. Hence the prime factors of 1225 are 5, 5, 7, 7.

Can a number be factored into a prime number?

This theorem states that natural numbers greater than 1 are either prime, or can be factored as a product of prime numbers. As an example, the number 60 can be factored into a product of prime numbers as follows: 60 = 5 × 3 × 2 × 2 As can be seen from the example above, there are no composite numbers in the factorization.

How are prime numbers used in number theory?

Prime numbers are widely used in number theory due to the fundamental theorem of arithmetic. This theorem states that natural numbers greater than 1 are either prime, or can be factored as a product of prime numbers. As an example, the number 60 can be factored into a product of prime numbers as follows:

Which is the best way to conduct prime factorization?

Prime decomposition: Another common way to conduct prime factorization is referred to as prime decomposition, and can involve the use of a factor tree. Creating a factor tree involves breaking up the composite number into factors of the composite number, until all of the numbers are prime.