Question

prove that 7- 2 root 2 is irrational if root 2 is irrational

Answer 1

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.

hope it is helpful!!!!

Answer 2

Answer:

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, 7- 2 root 2 is an irrational number.