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Irrational Numbers are the never-stay-still numbers!


Yes, irrational numbers are encountered in junior high school. These are like those friends of yours who never stay still in one place.

Our mathematical definition is that irrational numbers have decimal expansions that keep on going. They are not rational numbers that can be shown as a simple fraction (one integer divided by another – except zero of course).

For example, the square root of 2, is equal to 1.414213562… and on and on forever.

In other words, irrational numbers require an infinite number of decimal digits to write—and these digits never form patterns that allow you to predict what the next one will be. 

I like to think of these irrational numbers as ones that are never quite fixed in one exact spot on the real number line. They move (or vibrate like a plucked string) and the closer you look at them the more they seem to move. For example, we know that pi = 3.14 but, when we get even closer to pi, it becomes 3.14159. Get even closer and it is now 3.14159265, etc. So it has moved further and further to the right of its earlier place on the number line!!

These irrational numbers are really, really important numbers in Mathematics!

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NCEA Level 2 Algebra Problem. Using the information given, the shaded area = 9, that is:
y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]

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