prove that √5 irrational number
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Let √5 be a rational number.
Squaring on both sides,
p² is divisible by 5.
So, p is divisible by 5.
Squaring on both sides,
Put p² in equation(1)
So, q is divisible by 5.
Thus p and q have a common factor of 5.
So, there is a contradiction as per our assumption.
We have assumed p and q are co-prime but here they a common factor of 5.
The above statement contradicts our assumption.
Therefore, √5 is an irrational number.
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