Question

Show √7 - √11 is a irrational number

Answer 1

Answer:

Step-by-step explanation:

First we have to prove either √7 or √11 irrational

https://www.quora.com/If-%E2%88%9A11-is-irrational-how-can-you-prove-it  (how to prove √11 irrational)

https://brainly.in/question/401818  (how to prove √7 irrational)

after that,

let √7-√11 be rational number

∴√7-√11 = α/β         (here α and β are co-primes)

Now squaring both sides we get

18-2×√7×√11 = α²/β²        [ (a+b)²]

2×√7×√11= (18β²-α²)/β²

∴as √7 or √11 are irrational            .... (which ever you have proved write that)

Hence our assumption was Wrong.