Question

prove that (2-3√5) is irrational number​

Answer 1

Answer:

let 2-3/5 ia a rational no.

2-3/5 = p/q

-3/5 = p/q-2

-3/5 = p- 2q /q

/5 = p- 2q/-3q ............(1)

let /3 is a rational no.

/3 = a/ b

squaring both sides

3 = a2/b2

a2 = 3b2 ..........(2)

a2 is divisible by 3

a is also divisible by 3

a=3m

(3m)2 = 3b2

9m2 = 3b2

3m2 = b2 .......... (3)

b2 is divisible by 3

b is also divisible by 3

from (2) & (3)

/3 is an irrational number

so irritational cannot be equal to rational hence 2- 3/5 is an irrational number.