Question

Prove that 2 - root 3 is irrational

Answer 1

Let 2-√3 be rational

2-√3=p/q

√3=p/q+2

√3=(p+2q)/q(Integer/Integer)

√3 is a irrational number

it shows our supposition was wrong

hence 2-√3 is a irrational number
hope it helps u

Answer 2

Answer:

Here, the given number is,

2 - √3

Let us assume that 2 - √3 is a rational number,

Then by the property of rational number,

$2-\sqrt{3}=\frac{p}{q}$

Where, both p and q are integers, q ≠ 0,

$\implies \sqrt{3}=2-\frac{p}{q}$

$\implies \sqrt{3}=\frac{2-p}{q}$

Since, p and q are integers,

⇒ 2 - p and q are integers,

⇒ $\frac{2-p}{q}$ is a rational number such that q ≠ 0

But we know that √3 is an irrational number,

And, we can not equate a rational number and an irrational number,

Therefore, our assumption is wrong, 2 - √3 is not a rational number,

⇒ 2 - √3 is an irrational number.

Hence, Proved.