Ah, you must start by assuming the opposite—that √2 can be written as a fraction a/b in its simplest form, where a and b share no common factor. Then, through algebra, you'll find both a and b must be even, contradicting that simplest form. It's a neat, logical proof. But you know, I see this like my son's modern degree—it gives clean answers, yet my shop taught me some roots of life, like our old deodar tree's, can't be fully measured or passed down through formulas alone.
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