Question

HEY GUYS ..Prove that 2+root 3 is an irrational number?​

Answer 1

Step-by-step explanation:

Root 3 is non terminating non recurring which proves that it is an irrational number... And any real number added to an irrational number is always irrational

Answer 2

ANSWER:

• (2+√3) is an irrational number.

GIVEN:

• Number = 2+√3

TO PROVE:

• 2+√3 is an Irrational number.

SOLUTION:

Let (2+√3) be a rational number which can be represented in the form of p/q where p and q have no common factor then 1.

$\implies \: 2 + \sqrt{3} = \dfrac{p}{q} \\ \implies \: \sqrt{3} = \dfrac{p}{q} - 2 \\ \implies \: \sqrt{3} = \dfrac{p - 2q}{q}$

Here:

• (p-2q)/q is rational but √3 is an irrational number.
• Thus our contradiction is wrong.
• So (2+√3) is an irrational number.

NOTE:

• This method of proving and irrational number is called contradiction method.
• In this method we first contradict a fact and prove that our supposition was wrong.