This week in Pre-Calculus 11 I learnt how to rationalize a monomial and binomial denominator. Here is an example of rationalizing a monomial denominator:
The first step is to simplify the radical in the denominator. So, √12 can be further simplified into 2√3 and in the numerator the numbers inside the square roots cannot further simplify.
Here you take √3 and multiply it on the top and bottom of the question. Afterwards, you have to distribute it on the numerator and then multiply and multiply the √3 in the denominator
You can also see what number needs further simplifying such as the √9, which is just 3. Also, you have to multiply the 2 and the 3 which is 6.
Here you cannot further simplify the numbers inside the square roots but you can simplify the coefficients by dividing all of them by 3.
Here is the final answer:
Here is an example on how to rationalize a binomial denominator:
Take the conjugate of √2 – √5 which is just √2 + √5 and multiply it on the top and bottom. You have to use foil to multiply the top and bottom.
You can simplify this even further because both the √4 and √25 are perfect squares.
Plus, you can eliminate √10 and -√10 because they’re zero pairs. In addition, on the numerator both the √10 and √10 are liked terms, so you can add them together. You can add the 2 and the 5 on the numerator and minus the 2 and the 5 in the denominator.
You can take the minus sign from the denominator and multiply to the numbers in the numerator. Or, just leave it beside the fraction line.
Here are the final answers: