This week in PreCalc, we expanded on the ideas of radicals by learning how to add, subtract, multiply, and divide them. A lot of the ideas were straight forward, but the most challenging is dividing radicals.

Example:

Work:

Step 1: simply if necessary

Simplifying the given equation if it can be simplified makes the work easier later on because the numbers will be smaller.

Step 2: identify the conjugate

For dividing by a binomial, you have to multiply the numerator and the denominator by the denominators conjugate (is formed by changing the sign between two terms in a binomial). So the binomial in my example has a negative sign, but it’s conjugate will have a positive sign, and that’s the only difference between conjugates. The rest of the terms stay the same.

Step 3: multiply top and bottom by conjugate

Start with expanding the top and the bottom.

Step 5: simplify where necessary

After expanding, combine like terms, simplify radicals, and solve until you no longer can. When you can’t go any further, then you have reached your answer.