Question

2+root 3 2+ 3root 3 is rational or irrational give answer fast

Answer 1

If your question is 2+√3(2+3√3) then this is the answer,

First solve 2+√3(2+3√3)

=2(2+3√3)+√3(2+3√3)

=4+6√3+2√3+3(3)

=4+8√3+9

=13+8√3

Let 13+8√3 be a rational number.

A rational number can be written in the form of p/q where p,q are integers.

13+8√3=p/q

8√3=p/q-13

8√3=(p-13q)/q

√3=(p-13q)/8q

p,q are integers then (p-13q)/8q is a rational number.

Then √3 is also a rational number.

But this contradicts the fact that √3 is an irrational number.

So,our supposition is false.

Therefore, 13+8√3 is an irrational number.

13+8√3=2+√3(2+3√3)

Hope it helps