Question

show that 1 v2an irrational number
​

Answer 1

Answer-

 

Let us assume    is rational. 1/root 2

So we can write this number as

2

​  

 

1

​  

=  

b

a

​  

 ---- (1)

Here, a and b are two co-prime numbers and b is not equal to zero.

Simplify the equation (1) multiply by  

2

​  

 both sides, we get

1=  

b

a  

2

​  

 

​  

 

Now, divide by b, we get

b=a  

2

​  

 or  

a

b

​  

=  

2

​  

 

Here, a and b are integers so,  

a

b

​  

 is a rational number,  

so  

2

​  

 should be a rational number.

But  

2

​  

 is a irrational number, so it is contradictory.

Therefore,  

2

​  

 

1

​  

 is irrational number.

Step-by-step explanation:

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Answer 2

Answer:

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