Math 10 Honors Numbers Summary
In the last few weeks, our class has learnt a lot about Numbers and Radicals. Most of the material we went over was familiar, although there were a few things that were brand new to me.
Prime Factorization:
One of those things is how when you use prime factorization, it can help you to determine the prime factors that make up that number. Prime factorization is really helpful because you are breaking down the number to its smallest roots, and that can help you find out a lot about the number.
HOW IT WORKS:
You start with a number you want to prime factorize. You then begin to break it up into whole multiples of itself, and then break those multiples into smaller multiples, and you keep doing this until you end up with numbers that cannot be broken up into whole numbers any longer, otherwise known as Prime Numbers. These last prime numbers are the prime factors of your original number, which means if you multiply them all together, you should end up with the original number.
GCF & LCM:
Another example is how you can use prime factorization to find the LCM and the GCF.
GCF: This is the Greatest Common Factor between two numbers. The easiest way to find a GCF is to prime factorize 2 numbers. Once you have done that, you take out the common factors within both numbers and multiply those together to get the GCF.
LCM: This is the Lowest Common Multiple between two numbers. The easiest way to find a LCM is to prime factorize 2 numbers. Once you have done that, you take out all factors of both numbers, except for the ones common between the two numbers. Then you multiply those together to get het LCM.
Radicals:
I also learned the concept of turning entire radicals into mixed radicals, and vice versa. This is a neat trick for simplifying radicals and making them into easier numbers to understand and work with.
HOW IT WORKS:
Find a number that is not a perfect square, cube, etc. Take out a factor that is a perfect square or cube, etc, depending on the root of the radical. Once you have found a number, root it so it becomes a coefficient. Keep on dividing the number inside the radical until you have a number that is not divisible by the root anymore. You will then be left with a mixed radical.
Converting Mixed to Entire:
To convert a mixed radical into an entire radical, you basically take the coefficient and depending on the root, you square or cube, etc, it and multiply it with the number inside the radical. Then you are left with a larger, “entire” radical.
Those were the highlights for me in this unit. I found these 4 things very helpful and interesting, and I will definitely be using these tricks in the future.