Is a square root a rational number?

Answer 1

Some are and some are not.

For example, the square roots of 2.25, 3.61, 4, 4.84, 5.29, 6.76, 7.29, 8.41, 9, 10.89,

11.56, 12.25, 13.69, 14.44, 15.21, 16, 17.64, 18.49, 19.36, 20.25, 21.16, 22.09, 23.04,

24.5025, and 25 are all rational numbers.

But the square roots of 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22,

23, and 24 are Irrational Numbers.

We believe, but can't prove easily, that there are more irrational square roots

than rational ones.

Answer 2

A square root is considered a rational number if the number inside the square root sign is a perfect square. In other words, if the square root of a number results in a whole number, then it is a rational number. For example, the square root of 9 is 3, which is a whole number, making it a rational number. However, if the square root results in a non-terminating, non-repeating decimal, then it is considered an irrational number.