Question

Prove that 7+ 2√3 is an irrational number

Answer 1

Let 7+2✓3 is a rational number.

7 is rational and ✓3 is a irrational.

(7+2✓3)-7 is a rational. [ DIFFERENCE BETWEEN TWO RATIONAL NUMBER IS RATIONAL]


2✓3 IS RATIONAL.


2 IS RATIONAL AND ✓3 IS IRRATIONAL.


2×2✓3 IS RATIONAL. [ PRODUCT OF TWO RATIONAL NUMBER IS RATIONAL].


✓3 IS RATIONAL.


BUT THIS CONTRADICTS THE FACT ✓3 IS RATIONAL..


OUR ASSUMING IS WRONG.


HENCE,


7+2✓3 IS IRRATIONAL

Answer 2

Hope this answer helps you