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Question -

Prove that 4 – 5√2 is an irrational number. [CBSE 2010]



Answer -

Let 4 – 5 √2 is not are irrational number
and let 4 – 5 √2 is a rational number
and 4 – 5 √2 = a/b where a and b are positive prime integers
 
√2 is a rational number
But √2 is an irrational number
Our supposition is wrong
4 – 5 √2 is an irrational number

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