This week in precalculus 11 I was introduced to diving radicals, with this comes rationalizing the denominator. Rationalizing the denominator means eliminating irrational radicals from the denominator of a fraction, thereby converting it into an expression with only rational numbers (fractions or integers) in the denominator. This makes diving radicals way easier. To start we need to know what a conjugate is. Conjugate is changing the sign of a variable and conjugates are used to rationalize the denominator.
Example: if we have 234+47 the conjugate of this number is 234-47 (just changing the sign)
To rationalize the denominator, you need to multiply both the numerator and the denominator by the conjugate of the denominator.
Another example
we know that the conjugate of sqrt(2) – sqrt(3) is sqrt(2) + sqrt(3), so we multiplied the fraction by that. then we simplified the expression more by 2-3 and then we realized we have a negative denominator which is not good so we multiply everything by -1 so the negative denominator cancels out and we have a nicer number.
Always remember that you need to rationalize the denominator if the denominator is an irrational number