Question

Show that 7-√5 is irrational, give that √5 is irrational

Answer 1

Let us assume the contrary 7-√5 as rational number

Now

7-√5  =a/b

-√5    =a-7b/b

√5.    =-(a-7b/b)

√5.   =-a+7b/b

 √5.  =7b-a/b

7b - a /b is rational  number

Therefore √5 is also rational number

But it is given that √5 is irrational number

So our assumation is wrong