About: Proof that √10 is irrational   Sponge Permalink

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If √10 is a rational, say m/n, then m2 = 10n2. But in decimal notation, every square ends in an even number of zeros. So then m2 and 10n2 in decimal must end in respectively an even and odd number of zeros, a contradiction. Thus, If √10 is irrational.

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  • Proof that √10 is irrational
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  • If √10 is a rational, say m/n, then m2 = 10n2. But in decimal notation, every square ends in an even number of zeros. So then m2 and 10n2 in decimal must end in respectively an even and odd number of zeros, a contradiction. Thus, If √10 is irrational.
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abstract
  • If √10 is a rational, say m/n, then m2 = 10n2. But in decimal notation, every square ends in an even number of zeros. So then m2 and 10n2 in decimal must end in respectively an even and odd number of zeros, a contradiction. Thus, If √10 is irrational.
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