index laws
scientific notation
simplifying radicals
Always remember that to simplify, means to find an equation with the same value. To simplify a radical, you need to first find the largest perfect square that the the number inside the radical can be divided into, and then separate these into two radicals that multiply. Then reduce the perfect square to a whole integer, and put this outside of the radical symbol, and this is your final answer.
*If a radical doesn't have a perfect square as a factor, the expression is already in simplest form. |
multiplying radicals
To multiply radicals, you need to combine like terms, meaning whole integers together, and radicals together. Then you simply multiply these, first multiply the numbers outside, then the numbers inside. Always remember to simplify if possible. If the radical is a perfect square after multiplying, reduce that to its square root, and multiply it with any other integer outside the radical.
*Remember to always simplify the equation if possible, and multiply it with the remaining number outside the equation. In this example, 144 is a perfect square, so it can be reduced to 12, which is then multiplied with 6 to give the final answer: 72. |
Unit reflection
I consider this unit one of the hardest one we had this year, since radicals was something I have never studied in depth before. All the first part, relating the exponents and scientific notation, was something that I had already studied in previous years, only now we studied more deeply the exponents in the laws. Although I understood every step of multiplying radicals and simplifying them, I would do a small mistake, that would affect the whole process, and the answer. I had to practice these regularly, and by the second or third week of focus in this topic, I was able to simplify radicals much more easily.
***REAL-LIFE APPLICATION: Whenever I saw a radical symbol before, I would freak out, since I didn't know the value of it, or how to apply it to an equation, I didn't find these only in math class. I now know how to solve these, or turn them into a decimal if it is needed, although most of the times I can leave it as it is.
***REAL-LIFE APPLICATION: Whenever I saw a radical symbol before, I would freak out, since I didn't know the value of it, or how to apply it to an equation, I didn't find these only in math class. I now know how to solve these, or turn them into a decimal if it is needed, although most of the times I can leave it as it is.