Question

Is the square root of a natural number irrational

Answer 1

So it can be sometimes

Answer 2

The square root of a natural number can either be rational or irrational, depending on the square root itself.

- If the natural number is a perfect square (like 1, 4, 9, 16, etc.), then its square root is a whole number, which is a rational number. For example, the square root of 16 is 4, and 4 can be expressed as the fraction 4/1.

- If the natural number is not a perfect square (like 2, 3, 5, 6, 7, etc.), then its square root is irrational. For example, the square root of 2 is approximately 1.41421, and it cannot be expressed as a fraction of two integers.

In summary, the square root of a natural number is rational if the number is a perfect square and irrational if it is not.

Answer 3

Yes, exactly! The square root of a natural number can sometimes be rational and sometimes be irrational, depending on whether the natural number is a perfect square:

- **Rational**: If the natural number is a perfect square (e.g., 1, 4, 9, 16), then its square root is a whole number, which is rational.

- **Irrational**: If the natural number is not a perfect square (e.g., 2, 3, 5, 6, 7), then its square root cannot be expressed as a fraction of two integers, making it irrational.

So, to summarize, it can be both rational and irrational depending on the value of the natural number.