Show that 3+5root2 is an irrational number
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Let us assume that 3+5√2 is a rational no.
Thus 3+5√2 =p/q
5+√2 = p/q-3
√2 = p/5q-3
Hence, RHS is rational no.
Thus, LHS=RHS
LHS must be rational which isn't true as we all know that √2 is irrational number
That implies, our initial assumption 3+5√2 is rational no. isn't true
Hence, 3+5√2 is rational
Thus 3+5√2 =p/q
5+√2 = p/q-3
√2 = p/5q-3
Hence, RHS is rational no.
Thus, LHS=RHS
LHS must be rational which isn't true as we all know that √2 is irrational number
That implies, our initial assumption 3+5√2 is rational no. isn't true
Hence, 3+5√2 is rational
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