Question

prove that 7 minus 2 root under 2 is irrational

Answer 1

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Answer 2

let 7-2 root 2 be a rational number,
therefore, 7 -2 root 2 = p/q , where p and q are co-prime numbers.

take all the digits to the right hand side till you have only [root 2 ] , that is an irrational number left on the left hand side.

therefore, - 2 root 2 = p/q - 7
                 root 2 = 1/2 [ p/q - 7 ]

now .... LHS is not equal to RHS { LHS is an irrational number and RHS is a rational number}
this means that our assumption was wrong ...
therefore, 7- 2 root 2 is an irrational number.

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