Answer:
An irrational number produces an irrational when added to [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
To find : What number produces an irrational when added to [tex]\frac{1}{3}[/tex] ?
Solution :
We know that,
[tex]\frac{1}{3}=0.333....[/tex]
It is a rational number as it is repeating.
So, If we add a rational number into a rational number it always gives you a rational number.
To produce an irrational number,
If we add an irrational number to a rational number it always gives you an irrational number.
For example :
An irrational number - [tex]\pi[/tex]
A rational number - [tex]\frac{1}{3}[/tex]
Adding these two number,
[tex]\pi+\frac{1}{3}=3.47492598692...[/tex]
This number is non-terminating and non-repeating.
Therefore, An irrational number produces an irrational when added to [tex]\frac{1}{3}[/tex]
