In week four of Pre-Calculculus, eleven explored the ways to go about dividing and multiplying radical expressions. Using tactics such as the FOIL method and making sure you are multiplying the correct things together. When multiplying or dividing radical expressions, you must remember that coefficients go with coefficients, and radicands go with radicands. Meaning does not multiply or divide a coefficient with radicands. It is not correct.

An example that I will explain looks like this; (2√7 – 4√5)(3√7 + 2√50)
When going about this question, you can see if you can simplify it while the equation is still in brackets. For instance, over on the right of the equation, there is a 2√50. Since there is a perfect square, being twenty-five, in the root, it would make the question easier later if I made it a smaller number. Taking the perfect square of twenty-five and square rooting it, creating five, then multiplying by the coefficient. 5 x 2 = 10, and replacing the root for 2. Making the new expression 10√2.

The entire equation would now look like this; (2√7 – 4√5)(3√7 + 10√2)
Going from here, you start with the FOIL method, first, outer, inner, last. So, you would multiply 2√7 x 3√7 → 6√49. Then seeing you can simplify this since 49 is a perfect square, the expression then turns into √49 → 7 x 6 = 42.
Then you go to 2√7 x 10√2 → 20√14. Now we are halfway and can switch to multiplying the -4√5. Starting with -4√5 x 3√7 → -12√35, and ending with the foil method with -4√5 x 10√2 → -40√10. Create the new equation; 42+ 20√14 – 12√35 – 40√10.

After finishing the FOIL method and connecting all the new expressions, you would look for any simplifying you could do. If any of them had the same base we would add them together, or if any of the bases had perfect squares such as the expression 6√49 → 42 we did earlier. Since we do not have anything else to simplify, it is in its simplest form, and the equation is simplified.