Question

Prove that root 5 is an irrational number.

Answer 1

Answer:

बुलाती है मगर जाने का नहीं

Answer 2

Answer:

let assume root 5 is a rational number

root 5=a/b

on squaring both the sides, we get

5=a2/b2

a2=5b2

5 divides a2

5 divides a

So,we can take a=5m

a2=25m2

on putting value of a2 in a2=5b2 we get

25m2=5b2

5m2=b2

5 divides b2

5 divides b

5 is a rational number so it can divide with a and b and they are common integer but root5 is irrational it cannot divide with common integers a and b

so our assumption is wrong and root 5 is irrational.