Question

Prove that 3+2root3 is irrarional

Answer 1

Answer:

Let us assume that 3+2√3 is rational.

Therefore 3+2√3 =a/b,where a and b are co-primes and integers.

2√3=a/b+3

Take LCM

2√3=a+3b/b

√3= a+3b/2b

LHS= irrational

RHS=rational

LHS not equal to RHS

This contradicts the fact that √3 is irrational.

This contradiction is due to our wrong assumption.

Therefore 3+2√3 is irrational.

Hope it helps.

Answer 2

3+2root3 is equal to 6.4641

Since, it is non terminating and non recurring

Therefore, it is an irrational number