The square root of 2 is an irrational number because it cannot be expressed as a ratio or fraction, a/b, where a and b are whole-number integers, and b does not equal zero.
this is true but in simpler terms, it's b/c it's and on-going # just like pi (3.14.... and so on) and it goes on forever so there is no square root, so it is irrational.
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The square root of 2 is an irrational number
Sometimes the square root of a positive number can be irrational, as in the square root of 2 (which is a non-perfect square number), but sometimes it is a rational number, as in the square root of 25 (which is a perfect square number).
The square root of 3 is an irrational number
The square root of a positive integer can ONLY be:* Either an integer, * Or an irrational number. (The proof of this is basically the same as the proof, in high school algebra books, that the square root of 2 is irrational.) Since in this case 32 is not the square of an integer, it therefore follows that its square root is an irrational number.
This is impossible to prove, as the square root of 2 is irrational.