Question

Prove that √3-√2 is an irrational number.

Answer 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

Answer 2

Assume that root 3 and -root 2 is rational no.

than root3 -root2=p/q