prove that 3-3√5 is a irrational number
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let us assume that√5 is rational
√5=p/q, where p and q are co prime
squaring both sides
5=p^2/q^2
5q2=p^2
q^2=p^2/5 -------------(i)
=>p^2 is divisible by 5
=>p is divisible by 5
p=5c
q2=(5c) ^2/3
25c^2/5
q^2=5c^2
c=q^2/5
=>q^2 is divisible by 5
=>q is divisible by 5
=>p and q have a common factor
this contradict our assumption
therefore, √5 is irrational
=>multiplication of rational and irrational is irrational
=>3√5 is irrational
=>difference of rational and irrational is irrational
therefore, 3-3√5 is irrational
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