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Squares & Square Roots
Squares
3
We say, “Three squared is 9. We write 3 X 3 = 9
The square of three means a Square with three units on each side. There are nine small squares covering a square of three.
Another way of writing 3 x 3= 9 is 32 = 9. The small raised 2 is called an exponent. 32 = The 2 tells you that 3 is used as a factor two times. The 3 is considered the base.
3
Getting Warmed Up
This square is a ___ X ___ square.
It has a total of ____ squares.
So we read it as ____ squared.
How do we write ___ squared? ____
Squares
• Perfect Squares are the answer you get when you multiply a number by itself.
• Imperfect Squares are the numbers between perfect squares.
• Number your paper 1 – 12.
• Multiply each number by itself.
Example: 12 = 1x1=1
22 = 2x2=4
These are perfect squares .
• Create a table with the first 12 perfect squares and their square roots.
Perfect Square
1 4
Square Root
or Base
1 2
Square Roots
• In mathematics, certain operations are opposites of each other. One operation “undoes” the other.
Subtraction undoes Addition 12 + 3 = 15,
so 15 – 3 = 12
Division undoes Multiplication 4 x 6 = 24,
so 24 / 6 = 4
Square Roots
The opposite, or undoing, of squaring a number is finding the square root.
• A radical sign √ , is the symbol used to indicate the positive square root of a number.
• Ex: √36 = 6 , because 6 X 6 or 62 = 36
Square Roots
• Find each square root
• √81 = 9 because 9 x 9 or 92 = 81
• √225 = 15 because 15 x 15 or 152 = 225
When you are looking for the square root of a factor/number you are looking for the factor/number that was multiplied by itself to get the product under the radical sign.
Square Roots Guided Practice
• Find the Square of each number.1) 6
3) 17
• Find the Square root of each number.7) √121
20) √49