Question

give that √3is an irrational number prove that(2+√3)is an irrational number

Answer 1

$\bf{Given:- }$√3 is irrational.


$\bf{To prove :-}$ 2 +√3 is irrational


$\bf{Proof:-}$ Let 2+√3 be a rational number.

So, 2+√3 = a/b

√3 = a/b -2

a/b is a rational number and 2 is a rational number. We know that Rational number- rational number= Rational number. So, a/b -2 is rational.

But √3 is irrational.

This contradicts the fact that rational≠ irrational.

So, our supposition is incorrect.

Hence, 2+√3 is an irrational number.

$\bf{Hope\:it\:helps}$

Answer 2

Answer:

√3 is irrational.

2 +√3 is irrational

Let 2+√3 be a rational number.

So, 2+√3 = a/b

√3 = a/b -2

a/b is a rational number and 2 is a rational number. We know that Rational number- rational number= Rational number. So, a/b -2 is rational.

But √3 is irrational.

This contradicts the fact that rational≠ irrational.

So, our supposition is incorrect.

Hence, 2+√3 is an irrational number.

Step-by-step explanation: