This is impossible to prove, as the square root of 2 is irrational.
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No; you can prove the square root of any positive number that's not a perfect square is irrational, using a similar method to showing the square root of 2 is irrational.
The square root of 2 is an irrational number
Sometimes it is and sometimes it isn't. The square root of 2 and the square root of 3 are both irrational, as is their product, the square root of 6. The square root of 2 and the square root of 8 are both irrational, but their product, the square root of 16, is rational (in fact, it equals 4).
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.
Yes, it does, It is irrational, but it really is the square rootof 2.