Question

prove that 1/√2 is irrational
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Answer 1

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

qis 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