Question

When do you need to rationalize the denominator? My physics teacher says that you don't have to if you are isolating a variable.

Answer 1

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,

$\frac{1}{1+\sqrt{2} }$ (here the denominator is an irrational number)

Multiply the numerator and denominator by $1-\sqrt{2}$

We get $\frac{1-\sqrt{2} }{(1+\sqrt{2})(1-\sqrt{2}) }$

Here (1+\sqrt{2})(1-\sqrt{2}) = -1

Thus we get $\sqrt{2} -1$

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.

$a = \frac{x}{1+\sqrt{2} }$

Then we can say,

$x = a(1+\sqrt{2})$

No rationalisation required