Question

prove that 2√2-3 is irrational

Answer 1

let us assume that 2root2-3 is a rational number
2root2-3 = a/b ( a and b are integers , b not equal to 0 , a and b are co-prime)
or,2root2 = a-3b/b
or,root 2 = a-3b/2b

since , a , b,3,2 are integers then a-3b/2b is a rational number . so, root 2 is also a rational number but,root 2 is an irrational number . this contradiction has arisen because of our incorrect assumption .
therefore, 2root2-3 is an irrational number. (proved)


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