Question

Sam said the square root of a rational number must be a rational number. Jenna disagreed. She said that it is possible that the square root of a rational number can be irrational. Who is correct and why?

Answer 1

Jenna is correct.  This is because the square root of 2 is an irrational number.  And if the number is a prime number, the answer is less likely to have a rational square root.

Answer 2

Answer: Jenna is correct.

Step-by-step explanation:

We can prove this statement with help of two examples.

Since we know that 64 is the rational number.

And, the square root of 64 is $\sqrt{64}$.

Which is equal to 8 or -8.

And, they are integers, and we know that the integer are always a rational number.

Therefore $\sqrt{64}$ is a rational number.

And, If we take a number 2 which is a rational number.

Since, when we do square root of 2, we get √2.

And, √2 is a irrational number.

Thus, we can say that we can obtain a rational or irrational number after doing the square root of rational number.

Therefore, Jenna is correct.