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

When the denominator is an irrational number in order to make the denominator a rational number we rationalize the denominator.

Explanation:

For example,

`(1)/(1+√(2) )` (here the denominator is an irrational number)

Multiply the numerator and denominator by
`1-√(2)`

We get
`(1-√(2) )/((1+√(2))(1-√(2)) )`

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

Thus we get
`√(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 = (x)/(1+√(2) )`

Then we can say,

`x = a(1+√(2))`

No rationalisation required