Prove that (√2 + √3) is an irrational number, it is given that √2 is an irrational number.​

1 thought on “Prove that (√2 + √3) is an irrational number, it is given that √2 is an irrational number.​”

1. Answer:

   Let √3 – √2 be a rational number , say r

   Then √3 – √2 = r

   On squaring both sides we have

   (√3 – √2)2 = r2

   3 – 2 √6 + 2 = r2

   5 – 2 √6 = r2

   -2 √6 = r2 – 5

   √6 = – (r2 – 5) / 2

   Now – (r2 – 5) / 2 is a rational number and √6 is an irrational number .

   Since a rational number cannot be equal to an irrational number . Our assumption that

   √3 – √2 is rational is wrong

   Reply