Monboss, Scribe Post, Chapter 8

Howdy Guys,

Today we began a new chapter; Chapter 8: The Pythagorean Theorem and Special Right Triangles. We started class by exploring and looking into what exactly is the Pythagorean Theorem. The Pythagorean Theorem was developed by the philosopher and mathematician Pythagoras.




What is the Pythagorean Theorem?
Pythagoras proved that every right triangle square is
a^2 + b^2 = c^2
or
(leg)^2 + (leg)^2 = (hypotenuse)^2

Here's an example to show the equations use:




The figure above shows us the use of the equations because the number of squares around one side or leg of the triangle added with another side or leg of the triangle equals the hypotenuse, which is the sum of the two legs.

Example of the use of the Pythagorean Theorem:
(a)^2 + (b)^2 = (c)^2
(2)^2 + (3)^2 =(c)^2
4 + 9 = c^2
(squar. root)13 = (squar. root) c^2
c = (squar. root) 13

The Importance of Perfect Squares in the Pythagorean Theorem
It is important to know your perfect square, numbers that you will get if you multiple two numbers that are the same together ( e.g. 2*2, 3*3, etc.), because a lot of times you will need to simplify a number under the radical.

For example:
(2)^2 + (4)^2 = c^2
4 + 16 = c^2
20 = c^2
(squar. root)20 = (squar. root)c^2
now this is where some people will stop and believe the problem is over; however, using perfect squares we can simplify (squar. root)20 to:
(squar. root)4 (squar. root)5 = c
using my knowledge of squares, i know that the square root of 4 is 2 giving me:
c = 2 (squar. root)5

Now you are probably wondering how did i figure out that 4 and 5 will allow me to simplify (squar. root)20. Well this where the importance of knowing your Perfect Squares is vital.
Here are the Perfect Squares till 15:

4
9
16
25
36
49
64
81
100
121
144
196
225

Well young lads and young ladies that is all is I have for you.
May knowledge and strength be upon you.
Next Scribe Andrew

- Monboss