unit 1.2  squares and square roots
what do we need to know?
 Definition of a perfect square
 Know the perfect squares numbers (start with 1 to 144)
 Definition of a factor and how to get them
 Know the perfect squares numbers (start with 1 to 144)
 Definition of a factor and how to get them
class notes




more information
Let's review the concept of PERFECT SQUARE numbers:
the relationship between perfect squares and square roots
Here is a chart of the first 50 perfect square numbers, and their corresponding square roots:
factorization and perfect squares
Let's review:
It turns out, we can determine whether a number is a perfect square number if we look at its number of factors. Let's look at the following examples:
If you count the factors of 24, you will see that there are a total of 8 factors, an EVEN number of factors. But if you count the factors of 36, you will see that 36 has 9 factors, an ODD number of factors. This particularity is always true, and it allows us to determine which numbers are perfect squares:
All perfect square numbers have an ODD number of factors.
All nonperfect square numbers have an EVEN number of factors.
Let's try:
All perfect square numbers have an ODD number of factors.
All nonperfect square numbers have an EVEN number of factors.
Let's try:
Which one are perfect squares?
patterns for calculating square roots: Multiples of 100
We can use what we have learned so far to calculate the square root of numbers which are multiples of 100. This will work if:
 The number has an EVEN amount of zeroes, AND
 The first number (the number before the zeroes) IS A PERFECT SQUARE
 The number has an EVEN amount of zeroes, AND
 The first number (the number before the zeroes) IS A PERFECT SQUARE
Let's try these:
a different approach to finding the square root of a number
A number can be broken down into factors which themselves are perfect square numbers. For example:
Because you can break any number whichever way helps you get a square root, we can apply square roots to addition and subtraction:
Take a look at how perfect squares, areas and square roots are linked
videos that can help
online interactive activities
worksheets







review  workbook
math_8__unit_1.2.pdf  
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