Question

Is it possible to find the square root of a non-perfect square integer using the prime factorization method?

• A. Yes
• B. No

Answer 1

The correct option is B No

Let's see if we can use the prime factorization method to find the square root of a non-perfect square number, say, $450.$

Prime factorization of $450=2\times 3\times 3\times 5\times 5$ as elaborated below.

• To get the square root of a number by prime factorization method, all distinct prime factors of the number should be in pair.
• Here, the prime factors $3$ and $5$ are in pairs but $2$ is not in pair.

$450=2\times \underset{–}{3\times 3}\times \underset{–}{5\times 5}$

• As a result, the prime factorization method cannot be used to get the final result of the square root of a non-perfect square integer.

Hence, option (b.) is the correct answer.