The lessons in the third week of Pre-Calculus 11 were shortened due to a unit test. Nonetheless, one new topic that I learned was how to write mixed radicals as an entire radical. For instance, in question 3c, 5∜3 can be expressed as follows:
In reverse, radical expressions can be simplified. In question 4b):
During the simplification of a radical expression, caution must be taken in reading the index of the radical. I found that I tended to default my calculation to finding the ‘perfect square’ from the coefficient and variable and later realized that the index was something different. For this reason, I must often remind myself to slow down and scan the entire expression or equation to determine the index. Next, I will identify the factors based on the index of the radical. For example, if the index is 3, the factors must be cubed. Once this step is completed, I can confidently complete the calculation. Below is an example how to factor the coefficient/variable outside the radical.
The example below is a perfect example of my mistake. When I started to re-write the radical into a mixed radical, I first tried to find the square root of -48, c5, and 125. After using the factor tree for both -48 and 125, I knew something went wrong. Looking more thoroughly at the expression, I was dumbfounded. The whole root was supposed to be a cube root. Everything made sense now! The factoring inside the radicand was easier which allowed me to put the coefficients and variables outside with ease. This re-writing exercise became much simpler. I took this experience and double-checked each exercise in the next lesson called “Adding and Subtracting Radical Expressions.”
