Category: Math 11

This week in Pre Calculus 11, we learnt how to solve roots with variables. See picture below for example.

Questions that don’t work out as well should be written like this.

This wraps up our third week of Pre Calculus 11.

This week in precalculus 11, I learnt that when ever you see a fraction as an exponent in a question, it resembles a root and an exponent. The denominator of the fraction represents the root, and the numerator represents the power of the number. I’ll show this in a picture so it makes more sense. See picture below.

I also discovered the easiest way for me to solve an equation like this. When working with these types of questions, you can either root the number first or do the power first, it doesn’t matter which one to do first. I realized that when rooting a number, it gets smaller and when powering a number, it gets bigger. I prefer to square numbers when they’re as small as possible so the product isn’t as big of a number and daunting, so I root the number first, then do the power. See picture below.

This concludes week 2 of pre calculus 11.

In this first week of Pre Calculus 11 I’ve learnt a lot about rooting. Specifically, I learnt about negative square rooting and cubed rooting. Last year in math 10, we touched on the topic of basic square rooting, but I didn’t get the chance to learn about cubed or negative rooting. I found it fascinating that square rooting with negative numbers was impossible. I thought the number would become positive because normally when you multiply two negative numbers, they turn positive, but not in this case. The number is simply considered irrational and not possible to calculate. This is because when you are square rooting a number, you are finding what 2 same numbers square would equal the radicand. This would mean you have to use either 2 negative numbers or 2 positive numbers. When you multiply 2 numbers with like signs (+ or -), they will always equal a positive number (+).

On the flip side of things, it is however possible to cube root negative numbers. This is simply because you aren’t working with 2 numbers, you are working with three numbers. Following the same rules as square rooting, you must always use the same number with like signs (+ or -). If you multiply 3 numbers with the same negative sign, they will equal a negative number weather they’re they all the same number or not. Look at the following photo for an example.

This wraps up week one of Precalculus 11.