Question

prove that each of the following numbers is irrational
$\sqrt{5 - 2}$
​

Answer 1

Answer:

The steps are:-

Step 1:- Open a browser

Step 2:- Ask this question

Step 3:- You'll get your answer

Answer 2

Answer :-

$\bold{\sqrt{5}-2}$ is irrational number.

Step-by-step explanation :-

Given :

$\bold{\sqrt{5}-2}$

To find :

To prove that $\bold{\sqrt{5}-2}$ is irrational.

Solution :

Let $\bold{\sqrt{5}-2}$ be a rational number.

$\rightarrow \bold{\sqrt{(5-2})^2}=\bold{x^2}$

$\rightarrow \bold{5+4-2\times2\times\sqrt{5} }=\bold{x^2}$

$\rightarrow \bold {9-x^2}=\bold{4\sqrt{5}}$

$\rightarrow \bold{\sqrt{5}}=\bold{\frac{9-x^2}{4}}$

Here, we have x , x², 9 - x², 9 - x²/4 as rational numbers.

But √2 is an irrational number.

So,  x , x², 9 - x², 9 - x²/4 become irrational.

Our assumption is wrong.

∴ $\bold{\sqrt{5}-2}$ is irrational number.