Question

show that (√3 +√5)^2 is irrational number ​

Answer 1

Answer:

Step-by-step explanation:

Qⁿ : PROVE THAT ( √3 +√5 )² IS IRRATIONAL

SOLⁿ:

Let us assume to the contrary that  (√3 +√5 )² is rational number

Then (√3 +√5 )² = a/b ( a and b are positive integers, b≠0)

( a + b )² = a² + 2ab + b²

(√3 +√5 )² = (√3)² + 2 (√3) (√5) + (√5)²

                  = 3 + 2√15 + 5

                     = 8 + 2√15

8 + 2√15 = a/b

2√15 = a/b - 8

2√15 =   a - 8

                b

√15 =       a - 8

                 2b

 a - 8      

     2b         is rational number, then √15 is also rational number . But we    

               Know that √15 is irrational number . This is a contradiction . This  

                   contradiction has arisen from our incorrect assumption .

                SO WE CONCLUDE THAT  (√3 +√5 )² IS IRRATIONAL NUMBER