Question

prove that 5 - root 3 is irrationalb

Answer 1

Let us assume that 5 - √3 is rational number.

5 - √3 = $\dfrac{a}{b}$

Here a and b are co-prime numbers.

- √3 = $\dfrac{a}{b}$ - 5

- √3 = $\dfrac{a\:-\:5b}{b}$

Here;

$\dfrac{a\:-\:5b}{b}$ is rational number.

So, - √3 is also a rational number.

But we know that √3 is irrational number.

So, 5 - √3 is also a irrational number.

So, our assumption is wrong.

5 - √3 is irrational number.