Question

Prove that 2+root 5 is irrational

Answer 1

If possible, let us assume 2+

5

is a rational number.

2+

5

=

q

p

where p,q∈z,q



=0

2−

q

p

=−

5

q

2p−p

=−

5

⇒−

5

is a rational number

∵

q

2q−p

is a rational number

But −

5

is not a rational number.

∴ Our supposition 2+

5

is a rational number is wrong.

⇒2+

5

is an irrational number.

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