3 Prove that 3 is an irrational number. Hence, show that 7 + 2V3 is al

1.	3 Prove that 3 is an irrational number. Hence, show that 7 + 2V3 is also an irrational numberOR
Answer» 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

3 Prove that 3 is an irrational number. Hence, show that 7 + 2V3 is also an irrational numberOR

Answer»

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