Question

4.
Prove
that root 2-3 root 5 is an irrational no.​

Answer 1

Answer:

1. Let root 2 be rational.

• Then we can get two integers a and b (b is not equal to 0) such that
• root 2 =a/b
• root 2b=a
• root (2b)2=a2
• 2bsquare = a2
• Therefore,a2 is divisible by 2 so a is also divisible by 2.
• Let a=2c
• 2b2= a2
• 2b2=2c2
• 2b2 =4c2
• b2=2c2
• Therefore,b2 is divisible by 2 so bis also divisible by 2.
• Therefore, root 2 is irrational