Question

prove that
$1 \div \sqrt{2 }$
is irrational... ​

Answer 1

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

But p and q are coprime

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

∴1/√2 is irrational

Answer 2

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