Question

1. Prove that V3 - V5 is an irrational number.

Answer 1

Answer: here's my proof

Step-by-step explanation:

Let's pretend √3- √5 is rational, then √3- √5 = a/b , which a and b are coprime.

then 3- 2*√3*√5 +5 =  a^2 / b^2

       b^2 (2 (4 - √15)) = a^2

since a^2 is divisible by 2 , a also must be divisible by 2 so we can rewrite a as 2n :  

     b^2 (2 (4 - √15)) = 4n^2

      b^2 (4 - √15) = 2n^2

since b^2 is divisible by 2 , b also must be divisible by 2 so we can rewrite b as 2m. b= 2m and a= 2n. We know that a and b must be coprime so here it is proved.