wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Question 3 (i)
Prove that 12 is irrational.


Open in App
Solution

Let's assume that 12 is a rational number.
So, we can write this number as
12=ab
Here, a and b are two co prime numbers and b is not equal to 0.
Multiply by 2 both sides we get,
1=a2b
Now multiply by b,
b=a2
Divide by a we get,
ba=2 ---(i)
Here, a and b are integers, that means ba is a rational number. Then, 2 should also be a rational number as ba=2.
But, we know that 2 is an irrational number.
So, our assumption is wrong.
Hence, 12 is an irrational number.


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon