Question

Given that √7 is irrational prove that 3+4√7 is an irrational

Answer 1

√7 is irrational. (given)
now
3+4√7 let this be also rational.
3+4√7 = r
4√7= r-3
√7 = r-3/4
now, given that √7 is irrational. It means LHS i.e r-3/4 is also irrational. Here we contradicts and 3+4√7 is irrational.
Hope it may help u.......

Answer 2

If it is given that √7 is irrational, then we can prove above by the method of contradiction.
For this, First let
3+4√7 = r(rational)
4√7 = r-3
√7 = r-3/4
Now, √7 is irrational.
so, r-3/4 is also irrational.
Here we contradicts and 3+4√7 is irrational...