Question

prove √3 + √5 be a irrational number

Answer 1

do the same for √3 also
hope this helped u

Answer 2

Answer:

Step-by-step explanation:

Let us assume that sqrt3×sqrt5 is rational no.

So sqrt3×sqrt5 =p/q where pandq are coprimes.

Sobs

So 3×5=p^2/q^2

Therefore because of the above equation it is a contradiction and now sqrt3×sqrt5 is irrational.

Now

Sqrt3+sqrt5let them be rational

So sqrt3 +sqrt5=p/ qwhere pandq are coprimes

Sobs

Applying (a+b)^2

3 + 5 + 2 (sqrt 3×sqrt5)= p^2/ q^2

Take everything on right hand side (rhs)

Except sqrt3×sqrt5

Now lhs is irrational but rhs is rational this is a contradiction

Hence sqrt3+sqrt5 is irrational

Hence proved