Question

prove that one upon root 2 is an irrational number​

Answer 1

Answer:

irrational because root2 is irrational

Answer 2

Answer:

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 bothe side,

(1/√2)2 = (a/b)2

=> 1/2 = a2 /b2

=> 2a2 = b2

So b2 is an even number

=> b must be an even number

Let b = 2c

On squaring both side,

=> b2 = (2c)2

=> b2 = 4c2

now from equation 1

2a2 = 4c2

=> a2 = 2c2

=> 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.

Hense 1/√2 is an irrational number.

Step-by-step explanation:

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