Question

$prove \: that \: 3 + 2 \sqrt{5 \: is \: irrational \: number}$

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Answer 1

we have to prove 3+2√5 is irrational no

let us assume the opposite

I.e 3+2√5 is rational no

hence it can be written in the form of a/b

where a and b are not equal to zero and co prime

hence 3+2√5=a/b

2√5=a/b -3

2√5=a-3b/b

√5=a-3b/2b

here a-3b/2bis rational no

but √5 is irrational no

since rational is not equal to irrational

this is contradiction

therefore our assumption is wrong

hence 3+2√5 is irrational no