Fewpal
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Show that 5 + 3√2 is an irrational number.

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Solution: 
Let us assume, to the contrary that 5 + 3√2 is rational. 
So, we can find coprime integers a and b(b ≠ 0) 
such that 5 + 3√2 = a/b 
=> 3√2 = a/b - 5

=> √2 = (a - 5b)/3b 
Since a and b are integers,  (a - 5b)/3b is rational. 
So,  √2 is rational. 
But this contradicts the fact that √2 is irrational. 
Hence, 5 + 3√2  is irrational.

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