Prove that 6 - √7 is an irrational number, given that √7 is an

Q) Prove that 6 – √7 is an irrational number, given that √7 is an irrational number.

Ans: Let us assume that 6 – √7 is a rational number

Let 6 – √7 = $Prove that 6 – root 7$ ; q ≠ 0 and p, q are integers

$Prove that 6 – root 7$ √7 = $Prove that 6 – root 7$

Since, p and q are integers; Therefore 6q – p is an integer

Therefore, $Prove that 6 – root 7$ is a rational number

$Prove that 6 – root 7$ √7 is a rational number

But it contradicts given condition that √7 is an irrational number

Therefore, 6 – √7 is an irrational number………… Hence Proved !

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