Question

Prove that root 3 is an irrational number.
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Answer 1

Answer:

suppose 3–√3 is rational, then 3–√=ab3=ab for some (a,b)(a,b) suppose we have a/ba/b in simplest form.

3–√a2=ab=3b23=aba2=3b2

if b is even, then a is also even in which case a/b is not in simplest form.

if b is odd then a is also odd. Therefore:

ab(2n+1)24n2+4n+14n2+4n2n2+2n2(n2+n)=2n+1=2m+1

Answer 2

Answer:

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