2/√5 is an irrational number
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Proof:-
let 2/√5 is a rational number
A rational number can be written in the form of p/q
2/√5=p/q
√5/2=q/p [reciprocal]
√5=2q/p
p, q are integers then 2q/p is a rational number
Then, √5 is also a rational number
But this contradicts the fact that √5 is an irrational number.
So, our supposition is false
Therefore,
2/√5 is an irrational number.
Rationalising denominator :-
2/√5*√5/√5
=2√5/5
let 2/√5 is a rational number
A rational number can be written in the form of p/q
2/√5=p/q
√5/2=q/p [reciprocal]
√5=2q/p
p, q are integers then 2q/p is a rational number
Then, √5 is also a rational number
But this contradicts the fact that √5 is an irrational number.
So, our supposition is false
Therefore,
2/√5 is an irrational number.
Rationalising denominator :-
2/√5*√5/√5
=2√5/5
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