Question

prove that 3 + 2 root 5 is irrational​

Answer 1

Let's assume 3+2root 5 is a rational number.

Then we know rational number is in the form p/q

Then 3+2 root 5= p/q

=2root5=p-3q/q

= root 5=p-3q/2q

So p-3q/2q is a rational number so root 5 is also rational but we have already prove that root 5 is a irrational number. So our assumption is incorrect that 3+root 5 is a rational number so we conclude that 3+2 root 5 is an irrational number.

Hence Proved.

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