Question

prove that 4 minus 3 root 2 is an irrational number​

Answer 1

Consider, 4−3√2 Let 4−3√2 = (a/b) a rational number 
 ⇒ −3√2 = (a/b) − 4
⇒ −3√2 = (a − 4b)/b 
⇒ √2 = (a − 4b)/(−3b) 
Since a, b are integers,
then (a − 4b)/(−3b) represents a rational number. 
But this is a contradiction since RHS is a rational number where as LHS (√2) is an irrational number Hence our assumption that " 4−3√2 = (a/b) is a rational number" is incorrect.Thus  4−3√2 is an irrational number

Answer 2

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