prove that 5 root 2 + 3 is irrational
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Let us assume that 5+2 root 3 is rational
5+2 root 3 = p/q ( where p and q are co prime)
2root 3 = p/q-5
2 root 3 = p-5q/q
root 3 = p-5q/2q
now p , 5 , 2 and q are integers
p-5q/2q is rational
root 3 is rational
but we know that root 3 is irrational . This is a contradiction which has arisen due to our wrong assumption.
5+2 root 3 is irrational
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