Question

prove that root 5 is irrational , hence 3+2root5 is irrational

Answer 1

irrational numbers refer to incompleting numbers

√5 = 2.236............goes on
which is an irrational numbers. ..

3+ 2√5 = 3 + 2(2.236........)
=3+4.472.........
=7.472............. .
which is an irrational numbers


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Answer 2

Answer :

Given that, √5 is irrational.

Let us consider that (3 + 2√5) is rational and

3 + 2√5 = a/b, where a and b are integers with non-zero b.

⇒ 2√5 = a/b - 3

⇒ 2√5 = (a - 3b)/b

⇒ √5 = (a - 3b)/2b

Since, both a and b are integers (a - 3b) and 2b are also integers and thus (a - 3b)/2b be rational number.

But √5 being irrational, a contradiction is shown.

Thus, (3 + 2√5) is irrational. [Proved]

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