Question

Show that 5(3-2root11 divided by 7) is irrational number

Answer 1

Answer:

let

5(3-2root11 divided by 7) be rational number.

therefore,5(3-2root11/ 7) =a/b

3-2root11/7=a/5b

3-2root11=7b/5b

-2root11=7b/5b-3

3-7b/5b=2root11

By LCM,

(15b-7b)/5b=2root11

8b/5b=2root11

8b/10b=root11

4b/5b=root11

Because 4b/5b is an integer, it is rational

and so therefore root11 is also rational

But this is contradiction,

Because root11 is not a rational no.

So therefore 5(3-2root11/7) is an irrational number.