This Week I made a mistake with a question which included distributive property in it which is what I should have done the question looked like…

The original mistake I made is not realizing that distributive properties apply to this question, I guess I just got to hung over the radicals and everything I didn’t realize that distributive properties apply to it also, so what I originally did was just subtract the numbers inside the bracket and then plan to multiply the difference with √3, but that was just making the problem so much longer then it needed to be in which I got lost while doing and got it wrong obviously. Now, I will show the proper way to solve this.

So first,  we are obviously going to use distributive property for this problem which is going to make it easier so we are going to take √3 and then multiply it by all the radicals inside the brackets and when multiplying radicals, we already know to multiply the radicands together and the coefficients together, which will give us                2√18 – √36. Sorry I made a typo in the 2√12, its supposed to be 2√18.

Then, we see if we can simplify the two radicals anymore and since for 2√18, there is a perfect square that goes into that which is 9, so we take the square root of that number which is 3 and then multiply by the coefficient which is 2, while also leaving what remains as the radicand, so 2, so we get a simplified answer of 6√2. We then look at the √36 and since 36 itself is a perfect square, we write the answer to it down as 6 but you can see there is a negative coefficient so it becomes -6. Now, with all the simplified numbers and radicals, we get a final answer of 6√2 – 6.

One of the my best mistakes I made this week was when I was answering a question with a decimal radicand and decimal exponent. The question I’m referring to is…

The biggest mistake I made while solving that was solving it with decimals and lets just say I was on the question for around 10 minutes, now lets show the way I learned that made me realize that I was just complicating it for myself and making it harder on myself…

The first thing I did was to make both decimals into fractions and I already know that 0.81 into a fraction is just 81/100 and -1.5 as a fraction is -3/2.

Now that I have the fractions, I know that when I have an exponent as a fraction, then the denominator is going to be what I root the number by and the numerator of the exponent is going to stay as a power with the base, which gives me √81/100 with a -3 exponent, and since I know that when square rooting a fraction, you are simply just square rooting both the top and the bottom of the fraction, and the same applies to the exponent when it’s outside a bracketed number which means it applies to all the numbers in the fraction.

since I know that the square root of both 81 and 100 is 9 and 10, I’m left with 9/10 with -3 exponents on both top and bottom, since I know you can’t just have a negative exponent on a base and I got to make it positive, the way to do that is to reciprocate the fraction which mean flip it around so the numerator is now the denominator and vice versa, so now I’m left 10/9 with a positive 3 as an exponent.

Now that I’m left with a fraction with positive exponents, all I have to do is cube both the top and bottom which means multiply them by themselves 3 times, ex. 9x9x9 and 10x10x10. After, now I am left with my final answer of 1000/729.

My best mistake of the week was a question regarding converting a mixed radical into an entire radical but the coefficient was a negative number, and it looked like…

When looking at this question, I knew the fundamentals on how to solve it, since its a square root, I would have to take the coefficient and square it and then multiply it by the radicand, but, where I got wrong is it took the negative number as a whole, squared it and then multiplied that by the radicand which got me the answer √360 which is not the right answer, the real way to do it is…

As you can see in the example, instead of putting the negative number in the radicand, I left the – on the out side of the square root and just used the base number (6) to multiply in which got me my final answer of –√360.

One quote on the inspiration wall that really stood out to me was the one that said “1% better every day”. this stuck with me because it made me think about how this applies to both my sports and to math, because lets say if I was practicing soccer everyday, for a lot of people, they like seeing big results, and when they don’t, they get upset and even get unmotivated to train again which is why after reading this quote, I realize that you don’t need to be making big progress jumps after every time you practice something and shouldn’t get unmotivated when you don’t because it’s those same small percentages that add up over time. The same applies for math because if you are not good in a specific unit in math, then, if you practice everyday and get 1% better after every time you practice that unit, then all that is needed for you is consistency and in no time those 1%’s will add up and you will be an expert in that unit.