Question

prove that 2 + 3 root 5 is irrational ​

Answer 1

Answer:

let 2 +3/5 is a rational no.

2+3/5 = p/q

3/5 = p/q-2

3/5 = p- 2q/q

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

let /5 is a rational no.

/5 = a/b

squaring both sides

5 = a2/b2

a2 = 5b2 .............(2)

a2 is divisible by 5

a is also divisible by 5

let a = 5m

(5m)2 = 5b2

25m2 = 5b2

5m2 = b2 ..............(3)

b2 is divisible by 5

b is also divisible by 5

from (2) & (3)

/5 is an irrational number

so irrational no. cannot be equal to rational hence 2+ 3/5 is an irrational number.