Prove that√2×5isanirrationalnumber
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Step-by-step explanation:
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
2q−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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