I have run into a blogging problem. I haven’t had anything to talk about lately. Stuff to blog about comes in spurts. Have you noticed that? Well, to solve this problem, I have invited my friend, Melanie, the author of the now defunct blog, Duck Soup, to blog a post for me.
 I have to warn you, though, it is rated very high on the geeky scale. It is fascinating stuff if you like math. It makes your brain spin if you don’t. So, without further ado, I introduce Melanie…..

 (pause for the applause)


 The following came about as I was going through the Saxon Algebra 1 book.  You see, I don’t allow calculators and don’t plan on allowing it until calcus (if then).  Unfortunately, once you get to algebra, you start running into questions like this:  If the area of a circle is 53.23 squared, what is the a) radius and b) the circumference?  You need to be able to find the square root of whatever silly number you get when you divide 53.23 by 3.14 (which is what passes for pi in Saxon Algebra 1), but the book doesn’t teach how to do that without your handy dandy calculator.  So I had to figure it out myself.  It took me two days and six sources to get it (you all know that I am not a math person) but now I know it can be done, and it isn’t even all that time consuming.
 
To find the square root of any strange and wonderful wacko number (here we’ll use 549.3847):
 
First of all, we know the answer will be less than 24, because the square of 24 is 576, which is higher than our starting number, and higher than 23, because the square of 23 is 529, which is less than our starting number.  (Note to self:  It is very helpful to memorize perfect squares through 25.)  Keeping that in mind:
 
First divide the number into pairs, starting at the decimal point:
 
549.3847  would be:  5 49 . 38 47
 
Put the pairs under the usual division box.
 
Now find the largest square that will go into the first pair (which in this case is 5).  4 is the largest square which will go into 5, so write 4 under 5 and then subtract the difference.  Bring down the next pair, which is 49.  Put the square root of 4 (which is 2) above the five.
Now, double the numeral on top (which is two) and place it in parenthesis to the left of the remainder (which is 1 49) with a blank space next to it.  It’ll look like this: (4_) 1 49
 
Now find the largest digit to make 40 something times that same something is less than the remainder.  In this case, that something is 3, because 43 times 3 is 129; 44 times 4 doesn’t work because the product is greater than the remainder.  So, put 3 in the blank space and next to the 2 above the original number (5 49 38 47).  Subtract 129 from 149 and bring down the next pair, which will give you 20 38.
Now, double the number on top (23) to get 46.  Put that number in parenthesis to the left of the remainder (20 38) with a blank space next to it.  Like this:  (46_)  20 38
 
Okay, find the largest digit that will make four hundred sixty something times that same something is less than the remainder.  Here the something would be 4, because 465 times 5 is 2325, which is too high, and 463 times 3 is 1389, which is too low.  So write 4 in the blank space and up on top next to the 3.  Subtract 1856 from 2038 and bring down the next pair, which is 47.  This will give you 182 47.
Double the number on top (234) to get 468.  Place 468 in parenthesis to the left of the remainder with a blank space next to it.  (468_)  182 47
 
Now the something will be 3, because 4683 times 3 is 14049.  Write 3 in the blank space and up on top to the right of the 4.  Subtract 14049 from 18247 and bring down the next pair, which will give you 4198 00. 
 
Double the top number, which will give you 4686, and follow the above instructions until the desired accuracy is reached. 
I stopped at: 23.438
 
In Saxon, this would be rounded to: 23.44
 
(Another Note to Self: There is another method, called the Babylonian Method, which might be easier once the kids memorize those squares.  After memorization, teach them that method.) 
Advertisements