Questions & Answers

Question

Answers

A.True

B.False

C.Data insufficient

D.None

Answer
Verified

We need to check the given statement if true or not.

The statement is: The square of a prime number is prime.

Let us recall the definition of prime numbers. According to the definition, a prime number is a number which is only divisible by 1 and the number itself. Prime numbers are not divisible by any other number except those two (1 and itself).

Now, considering the square of the prime numbers, let us say a number m is a prime number. Therefore, its square will be $m^2$ .

Let us suppose $m^2$ is a prime number.

For $m^2$ to be a prime number, according to definition, it must contain only 2 factors i. e., 1 and $m^2$ .

But $m^2$ can also be written as mxm which makes m a factor of $m^2$ as well.

So, we get 3 factors of $m^2$ in total i.e., 1, m and $m^2$.

Hence, our assumption is wrong that the square of a prime number is also a prime number.

Therefore, we can say, by contradiction, that $m^2$ is not a prime number.

For example take the number as 3 square will be 9 . Here 3 is a prime number but 9 is not a prime number.

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