Question

Show that $2- {\sqrt{3}}$ is an irrational number

Answer 1

SOLUTION :  

Let us assume , to the contrary ,that 2 - √3 is rational. Then,it will be of the form a/b where a, b are co primes integers and b ≠0.

2 - √3 = a/b

2 - a/b = √3  

since, a & b is an integer so, 2 - a/b   is a rational number.  

∴ √3 is rational  

But this contradicts the fact that √3 is an irrational number .

Hence,  2 - √3 is an irrational .

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

hello...

Let 2 - √3 is rational.

✔️2 - √3 = a/b

✔️2 - a/b = √3  

here...
a & b is an integer so, 2 - a/b is rational. 

or ............
√3 is rational  

But this contradicts that √3 is an irrational number..... .

so.....

 2 - √3 is an irrational .


Thankyou....