Solving Radical Expressions.

MONSTER QUESTION. ahhh.
okay.
When i first looked at this question I was so confused and I didn't know where to start.
So I remembered what Mr.Cheng says about taking it one step at a time.
and start with little and work your way up. This is what I did
1. The first thing I did was get rid of the negatives. You do this by flipping them.
2. You distribute the exponent outside of the brackets
3. You are left with a fraction exponent so you distribute those too on the numbers.
4. Then you distribute the fraction exponent of the variables and turn the squares and exponents of the numbers into a number.
5.The square roots of the variables cancelled each other out and the exponent can both be divided by 2.
and then you have your answer.
YAY. not so hard.

Problem Solving #1

My favourit question from this weeks problem solving sheet was question #10.

The sum on nine consecutive numbers positive integers is 99. The largest of these integers is
(a)9 (b)11 (c)19 (d) 7 (e)15

When i first looked at this question i thought that the only way to solve it would be trial and error but that would take a long.
One way to solve it is with an arithmetic sequence. Which is what we have been learning for the past week.
the sequence would be

x+1, x+2, x+3, x+4.... x+9 =99

from that sequence you can get the following formula

9x+45=99
9x=54
x=6

you then use 'x' and plug it into the 9th term.

x+9
6+9 = 15

so the largest of the integers is 15.

What I especially liked about this question is that it has so many other way to solve it. I find it amazing because with these other ways you can also check you answers. I enjoy having to think hard to find these alternate answers. Some of these alternate ways are the following:

x-4, x-3, x-2, x-1, x, x+1, x+2, x+3, x+4

9x+99
x=11

and
x+4 =15
11+4 =15

and there you have your answer.

At first i was anoyed because i didnt know how to solve it and i was applying what i know to solve the question. I learned that you have look deeper and use what you have learned to solve questions like that. Thats what being good math is all about.

Tower of Hanoi

describe the strategy and the formula for the puzzle Tower of Hanoi
Embed a screen shot of the completed puzzle with 5 dics

To some, The Tower of Hanoi puzzle may seem like just another, regular, for fun game but really it is a challenging math puzzle that involves skill and strategic thinking in order to be solved. During math class we got the chance to try it out. It harder than it seems.

The first time I tried doing this it took me over a hundred times. It was until Mr. Cheng explained that there was a strategy to it that I started to think. I had not even considered the option of there being a strategy to it.
The strategy I came up with throught out my various attempts at trying to do this puzzle is that is to pile the first 4 in the middle first then move the 5th disc to the other side and pile the 4 on top.