Question

The square root of natural
Number is sometimes irrational

Answer 1

Yes, that's correct! The square root of a natural number can be either rational or irrational depending on the number itself.

1. **Rational Square Roots**: If a natural number is a perfect square (e.g., 1, 4, 9, 16, 25, etc.), then its square root is a rational number. For example:
- The square root of 4 is 2 (which is rational).
- The square root of 16 is 4 (which is rational).

2. **Irrational Square Roots**: If a natural number is not a perfect square (e.g., 2, 3, 5, 6, 7, 8, 10, etc.), then its square root is an irrational number. For example:
- The square root of 2 is approximately 1.414, which cannot be expressed as a fraction of two integers, making it irrational.
- The square root of 3 is approximately 1.732, also irrational.

In summary, the square root of a natural number is irrational when the number is not a perfect square.