Question

Prove that 2+ 3root3 is an irrational number

Answer 1

assume 2+3Root 3 be a rational no

. let 2+3root3 be x

Step-by-step explanation:

squaring on both sides

(2+3root 3 )^2 = x^2

2^2+3root3^2+2*2*3Root3=R^2

4+27+12Root3=r^2

root3= R^2- 31/12

.

so we found that LHS is irrational

but the RHS is rational no

so 2+3root3 is irrational no

our assumption is wrong