Month: September 2018

This week we focused on simplifying, evaluating, and solving radicals of all kinds.

Here is a video to give you an understanding:  https://www.youtube.com/watch?v=Ef2gOQbDv7M

We first started with simplifying addition and subtraction equations. The strategies for simplifying polynomials can be used to simplify sums and differences of radicals. Like terms or like radicals in a sum or difference of radicals have the same radicand and the same index.  pg. 111 For example, when we add 3 + 5 = 8, it is quite simple to see that they go together. When combining variables and radicals, it goes the same. Eg. 7a + 2a = 9a / 

Near the end of the week, we started getting into multiplying and dividing radicals in different forms. The strategies used to expand and simplify products of binomial expressions can be extended to include radicals with variables in the radicand. As with sums and differences, it is important to identify the values of the variables for which the expression is defined. pg.121 For example, when multiplying/ dividing, it is nearly the same as normal multiplying/dividing. Eg: 7 x 5 = 35 / 2√4 x 5√4 = 10√16

This week we have merged into a new chapter/section called absolute values and radicals. In this chapter, we learn the true values of numbers of all kinds, along with learning square roots and cubed roots. Our equations often combine a couple of these.

The absolute value of a real number is defined as the principal square root of the square of a number. For absolute values, we think it as numbers on a number line and valuing their distance from 0. As such, -4 would be 4 paces away from 0, making it actually 4. When in the brackets, negative numbers turn positive and positive stays positive.

For roots and radicals, a principal square root is when a squared number is equal to a whole number by itself. A non-perfect square root is when it does not equate to a sole whole number, rather transforming into an equation as such: √50 = 5√2. Only a few cubed roots can be whole (Q) but most are not.

We are usually practicing how to determine square roots that are not sole whole numbers and sometimes with added variables and exponents.

This week we “converged”, (little hint), into geometric sequences and whole new terms which were infinite or finite, and converging or diverging. They both are alike but produce different answers. It is crazy to think that we can calculate to infinite and determine the sum. I much enjoy geometric sequences, although, the infinite and finite equations will have to grow on me.