Question

prove that the following are irrational.i)1/√2.ii)√3+√5​

Answer 1

Answer:

Step-by-step explanation:

To prove 1/√2 is irrational

Let us assume that √2 is irrational 

1/√2 = p/q (where p and q are co prime)

q/p = √2

q     = √2p

squaring both sides

q²   = 2p²                                                  .....................(1)

By theorem 

q is divisible by 2

∴ q = 2c ( where c is an integer)

 putting the value of q in equitation 1

2p² = q² = 2c² =4c²

p² =4c² /2 = 2c²

p²/2 = c² 

by theorem p is also divisible by 2

This is a contradiction which has arisen due to our wrong assumption

∴1/√2 is irrational