Question

prove that √5-√3 is inrational number.

Answer 1

Answer:

Step-by-step explanation:

Let sqrt(3) be rational. sqrt(3) = p/q where p/q is irreducible fraction (otherwise we reduce it).

3=p^2/q^2

3q^2=p^2

So p^2 is divisible by 3, hence p is divisible by 3. Let p=3n

3q^2 = (3n)^2

3q^2 = 9n^2

q^2 = 3n^2

So, q^2 is divisible by 3, hence q is divisible by 3.