The Perfect Square
A perfect square is a number that has two identical factors. Ex. 36 = 6x6
What was a factor again?
Composite or Prime?
Let's Factor a number....
100
10 x
5 x 2
10
5 x 2
Looking at this... can we come up with the perfect
square for 100 from factoring??
Well, we need to gather the squares and multiply them
(5 and 5) (2 and 2)
5 x 2 = 10!
1
Let's try another one:
144
4 x 36
2 x 2
6 x 6
3 x 2 3 x 2
Let's gather the pairs
What do we get?
2
Let's try a number that we know isn't a perfect square:
48
12 x 4
No pair for three!
6 x 2 2 x 2
3 x 2 What makes this different from the perfect square example?
Note: The last digit of a perfect square will never be a 2, 3, 7, or 8!
3
Now, with algi­tiles, let's show pictorially how to evaluate
the following square root:
49
49
7
7
Think of perfect squares and their square roots as little squares making big squares:
The total number of little squares that form the bigger square is the perfect square = 49
The number of little squares on each side of the bigger square is the square root. 7 and 7 or 7 x 7
Let's try with algi­tiles:
100
64
25
4
But what about non­perfect squares?
Well... we have to estimate!
Sometimes it is impossible to place together little squares to form a bigger square. This means that the square root of the number will not be a whole number, so you need to estimate.
31
Which perfect square is 31 closest too? 25 or 36? Would the
square root be closer to 5 or 6? That is your estimate to the decimal
place!
31 little squares cannot be placed together to make a big square.
Draw extra squares from the perfect square or leave some squares missing to show your
work!
Try it with your algi­tiles ­ what do we get?
4
2
What is the Square Root of 5?
The perfect square 4 is closer to 5 than the perfect square 9.
So, I would draw this to show pictorially, the estimate for the Square Root of 5:
5
2
2
2
And I would say that it is approximately 2.2!
5
Tomorrow ­ how to estimate non­perfect squares!
without algi­tiles...
6