prove that[ 3 plus 2root 5 ]square is an irrational no

1.	prove that[ 3 plus 2root 5 ]square is an irrational no
Answer» We know that the sum of a rational and an irrational is irrational and the product of a rational and an irrational is irrational and √5 is irrational.So (3+2√5)^2=3^2+2×3×2√5+(2√5)^2=9+12√5+20=29+12√5Here 12√5 is irrational and hence 29+12√5 is irrational.

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