Question

√7 iz irrational prove it

Answer 1

Answer:

let, root 7 =a/b is a rational no{where a and b are co prime and b is not equal to 0}

b root 7 = a

squaring both sides , we get

7 b squared = a squared

therefore a squared is divisible by 7

so a is also divisible by 7

so we can write a = 3c where c is some integer

substituting for a we get 7 b squared = 49 c squared

b squared = 7 c squared

therefore b squared is divisible by 7

so b is also divisible by 7

therefore a and b have atleast 7 as a common factor

but a and b are co prime

so we conclude that root 7 is irrational

Step-by-step explanation: