Question

prove that √7 is irrational
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Answer 1

Answer:

HOPE IT HELPS YOU

Step-by-step explanation:

it is irrational as it is not a perfect square no.

Answer 2

heya mate ♥️

let us Assume that √7 is rational .Then, there exist co-prime positive integers

a and b such that

√7= a/b

➜ a=b√7

squaring on both side, we get

a² = 7b²

therefore, a² is divisible by 7 hence, a is also divisible by 7

so , we can write a= 7p , for some integer p,

substituting for a , we get

49p²=7b²

➜ b²=7p²

this means , b² is also divisible by 7 and also b divisible by 7

therefore , a and b have at least one common factor 7

but , this contradicts the fact that a and b are co- prime .

thus our suppositing is wrong .

hance , √7 is irrational .

hope it's help you ☺️