9) Prove that 3 +√ 5 is an irrational number.
Answers
Let us assume that 3+√5 is a rational number.
⇒3+5=pq
, where p and q are the integers and q ≠0.
⇒5=pq-3=p-3qq
Since p , q and 3 are integers. So,
p-3qq is a rational number.
⇒5 is also a rational number.
but this contradicts the fact that
5
is an irrational number.
This contradiction has arisen due to the wrong assumption that 3+5is a rational number.
Hence, 3+5 is an irrational number.
Prove that 3 + √ 5 is an Irrational Number. Concept: Concept of Rational Numbers.
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