Question

prove that √7 is an irrational number​

Answer 1

Answer:

let us assume that √7 be rational. then it must in the form of p / q [q ≠ 0] [p and q are co-prime]

√7 = p / q => √7 x q = p

squaring on both sides

=> 7q2= p2 ------> (1)

p2 is divisible by 7 p is divisible by 7 p = 7c [c is a positive integer] [squaring on both sides ] p2 = 49 c2 --------- > (2)

subsitute p2 in equ (1) we get 7q2 = 49 c2 q2 = 7c2 => q is divisble by 7 thus q and p have a common factor 7.

there is a contradiction as our assumsion p & q are co prime but it has a common factor. so that √7 is an irrational.

HOPE IT HELPS U...

Answer 2

Explanation:

let us assume that √7 be rational. thus q and p have a common factor 7. as our assumsion p & q are co prime but it has a common factor. So that √7 is an irrational.

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