Question

prove that is 2underroot 3 is an irrational number??​

Answer 1

Answer:

hope u get it

Step-by-step explanation:

Here, the given number is,

2 - √3

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

Then by the property of rational number,

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

and are co-prime i.e. no other factors rather than 1

Since, p and q are integers,

⇒ 2 - p and q are integers,

⇒  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.

Answer 2

first prove

$\sqrt{3}$

is irational then multiplication of rational and irational us alwyas irational