Answer:
When the denominator is an irrational number in order to make the denominator a rational number we rationalize the denominator.
Step-by-step explanation:
For example,
[tex]\frac{1}{1+\sqrt{2} }[/tex] (here the denominator is an irrational number)
Multiply the numerator and denominator by [tex]1-\sqrt{2}[/tex]
We get [tex]\frac{1-\sqrt{2} }{(1+\sqrt{2})(1-\sqrt{2}) }[/tex]
Here (1+\sqrt{2})(1-\sqrt{2}) = -1
Thus we get [tex]\sqrt{2} -1[/tex]
Here the denominator has become a rational number.
When we are isolating a variable we are only taking the required variables to one side thus it doesn't require rationalization.
[tex]a = \frac{x}{1+\sqrt{2} }[/tex]
Then we can say,
[tex]x = a(1+\sqrt{2})[/tex]
No rationalisation required
