Squares & Square Roots

Squares

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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.

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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