Question

What is the square root of 3025 using the prime factorization?

Answer 1

Hint: There are many methods to find the square root of a give number but in this question, we are going to see the prime factorization method. Prime factorizing means expressing a given number in terms of multiplication of prime numbers only. The method to find the square root of a number using prime factorization is explained below in detail.

Complete step-by-step answer:
In this question, we are given a number and we have to find its square root using the prime factorization.
Now, there are other methods too to find the square root of a number like the division method and the log method. But we are going to use the prime factorization method in this question.
First of all, let us see what square root is.
Square root of a given number is a number is the number which when multiplied by itself gives the original number. For example: Square root of 4 is 2 and when we multiply 2 by 2, we get the original number that is 4.
Method to find square root using Prime Factorization:
Step 1:
Prime factorize the given number. Prime factorization means expressing a given number in terms of multiplication of prime numbers only.
$ \Rightarrow 3025 = 11 \times 11 \times 5 \times 5$
Step 2:
The square root of the number will be a product of the prime numbers that occur twice.
Therefore, here, 11 and 5 occur twice.
$ \Rightarrow $Square root of 3025$ = 11 \times 5 = 55$
Therefore, the square root of 3025 is 55.

Note: Square root of a number is written under $\sqrt {} $ sign and this sign is called as radical and the value inside this sign is known as radicand. For example, the square root of 3025 is denoted by $\sqrt {3025} $ and 3025 is called radicand.