Prove that 5+2✓5 is a irrational number
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Let 5 be a rational number.
then it must be in form of qp where, q=0 ( p and q are co-prime)
p2 is divisible by 5.
So, p is divisible by 5.
So, q is divisible by 5.
Thus p and q have a common factor of 5.
We have assumed p and q are co-prime but here they a common factor of 5.
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