Question

prove that 1/root 2 is irr rational​

Answer 1

Explanation:

We will prove it by the method of contradiction.

Let 1/√2 is a rational number

So we can write 1/√2 = a/b .........1

where a and b are relatively prime numbers.

Squaring equation 1 on both sides,

(1/√2)^2 = (a/b)^2

=> 1/2 = a^2 /b^2

=> 2a^2 = b^2

So b^2 is an even number

=> b must be an even number

Let b = 2c

On squaring both sides,

=> b^2 = (2c)^2

=> b^2 = 4c^2

now from equation 1

2a^2 = 4c^2

=> a^2 = 2c^2

=> a must be an even number.

Now since both a and b are even numbers, then a and b can not be relatively prime.

So our assumption is wrong.

Hence, 1/√2 is an irrational number.

Answer 2

No........But I was playing....

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