Proof that 7+root5 is not a rational number.

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Solution

let 7+√5 be a rational no.
then 7+√5 = a/b , a and b are integers & b not equal to 0

√5 = (a/b)-7

√5=(a-7b)/b

√5= integer - 7 (integer)
Integer
=which is a rational no.

But √5 is irrational no.

So here it shows

LHS = Irrational and RHS = Rational

Therefore it is contradiction to our assumption
hence 7+√5 is irrational no.

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