Question

give that under root 3 isirratonal prove that 2 + root 3 irrationsl​

Answer 1

Answer:

Let 2+√3 an rational no.

So, we can write it in form of A/B

2+√3=A/B

√3=A/B-2

√3=A-2B/B

[•A,B are integers because 5B-A/B is a rational no]

As √3 is rational

Answer should be in form of prime no. But it is Co-prime no.

So, our contradiction or assumption is completely wrong and √3 is irrational. Hence, 2+√3 is an irrational.

Step-by-step explanation:

Answer 2

Answer:

Step-by-step explanation:

We assume that 2+root 3 is an rational numbers

2+root 3= p/q ( p, q €, z and q not equal to 0

HAD of p and q= 1

P and q is a Co prime number

2+ root3= p/ q

Root 3= p/q-2

Roor3=p-2q/q

Therefore root 3 is rational numbers and root 3= p-2q/q is an irrational numbers therefore our assumptions is wrong.

Therefore 2+root3 is irrational number