When students, in 7th grade, encounter the Pythagorean Theorem – a² + b² = c² –
they must also run into the concept of SQUARE ROOTS. So, lets get a historical
timeline of Math thus far.
Whole Numbers and Counting Numbers: These are good, I can count pennies
Fractions: OMG, just when I was getting used to counting you brake things into
halves, fifths, and tenths.
Decimals: Do I divide the bottom into the top or the other way?
Integers: Now you have me going "which way"?
Square Root or at times Irrational Numbers: Hay, I don't like irrational
people, why would I like irrational numbers. These numbers
cannot even be written as a fraction.
And with all of these we have the four basic operations that the student must
do with each. I know that you look at this list, and it is easy to say, "I will stick
to counting pennies". Folks it is only the 7th grade, and we have to add in
graphing, probability, statistics, equations and a few other notions.
Confused yet?
So, WHAT IS THE √2?
We know that 5² = 25, thus √25 = 5.
That means that √49 = 7. That is correct.
The square root of a perfect square is a whole number.
The √1 = 1 and the √4 = 2. That means that the √2 is between 1 and 2.
Now you understand. We are looking for a number between 1 and 2 that
when squared is the number 2.
This is when things begin to get sticky. Remember that value π or pi.
3.1415926535897932346...
Pi is a transcendental number, its decimal never repeats or terminates.
√2 is the same, 1.414213562...
If you square the value above you will get 1.99999999, close to but
not 2. Because we have this unending decimal we have no way of writing
this number as a fraction a ÷ b. Thus we call it an
IRRATIONAL NUMBER
The √3 is 1.7320508...
This is another irrational number. Now we must do our operations
with these numbers. Treat them like a variable, because you really
do not know what there true value is. I will discuss this on a separate
page.
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