Question

Prove that it is an √7
irrational number​

Answer 1

Answer:

Let us assume that root 7 is rational. Then, there exist co-prime positive integers a and b such that

Root 7=a÷b

a=b root 7

squaring both sides,

a2=7b2

therefore, a2 is divisible by 7 and 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 amd so, b is also divisible by 7

Therefore, a and b have atleast one common factor. ie, 7

But this contradicts the fact that a and b are co- prime

so, our assumption is wrong and root 7 is irrational..

I hope that this would help u❤️