Question

Prove that 5-5^1/2 is irrational.

Answer 1

REFER THIS QUESTION AND TRY THIS BY YOURSELF

prove that (3+2 root 5)square is irrational

see first let solve the question first

(3+2root5)² = (3)^2 + (2root5)^2 + 2(3)(2root5)

= 9 + 10 + 12root5 = 19 + 12root5

so let us now first take it as rational no.

means it will be equal to p/q where q is not equal to 0

so

19 + 12root5 = p/q

12root5 = p/q - 19

since ratinal no. subtracted from a rational no. gives rational no. so 12root5 should be rational but since any rational multiplied but irrationalno.(root5) gives irrational no.

so there is a contradiction

and hence

(3+2root5)² is irrational no.