Squares, Square Roots and Perfect Squares

Area of a Square

The area of a figure is the number of square units needed to cover the figure.

The area of the square below is 16 square units because 16 square units are needed to COVER the figure...

A = 42 = 4 4

= 16 sq.units

Area of a Square

The area (A) of a square can be found by squaring its side length, as shown below:

Click to see if the answer found with the Area

formula is correct!

A = s2

4 units

The area (A) of a square is labeled as

square units, or units2, because you

cover the figure with squares...

1 What is the area of a square with sides of 5 inches?

A

B

D

C

16 in2

25 in2

20 in2

30 in2

2 What is the area of a square with sides of 6 inches?

16 in2

24 in2

20 in2

36 in2

A

B

D

C

3 If a square has an area of 9 ft2, what is the

length of a side?

A

B

D

C

2 ft

3 ft

2.25 ft

4.5 ft

4 What is the area of a square with a side length of 16 in?

5 What is the side length of a square with an area of 196 square feet?

When you square a number you multiply it by itself.

52 = 5 5 = 25 so the square of 5 is 25.

You can indicate squaring a number with an exponent of 2, by asking for the square of a number, or by asking for a number squared.

What is the square of seven?

What is nine squared?

49

81

Make a list of the numbers 1-15 and then square each of them.

Your paper should be set up as follows:

Number Square 1 1 2 4 3

(and so on)

Number Square 1 1 2 4 3 9 4 16 5 25 6 36 7 49 8 64 9 81 10 100 11 121 12 144 13 169 14 196 15 225

The numbers in the right column are squares of the numbers in the left column.

If you want to "undo" squaring a number, you must take the square root of the number.

So, the numbers in the left column are the square roots of the numbers in the right column.

Square Root Square

1 12 43 94 165 256 367 498 649 8110

10011

12112

14413

16914

19615

225

The square root of a number is found by undoing the squaring. The symbol for square root is called a radical sign and it looks like this:

Using our list, to find the square root of a number, you find the number in the right hand column and look to the left.

So, the 81 = 9

What is 169?

Square Perfect Root Square

1 12 43 94

165

256

367

498

649

8110

10011

12112

14413

16914

19615

225

When the square root of a number is a whole number, the number is called a perfect square.

Since all of the numbers in the right hand column have whole numbers for their square roots, this is a list of the first 15 perfect squares.

Find the following. You may refer to your chart if you need to.

6 What is ?1

7 What is ?81

8 What is the square of 15 ?

9 What is ?256

10 What is 132?

11 What is ?196

12 What is the square of 18?

13 What is 11 squared?

14 What is 20 squared?

Day 13Squares of Numbers

Greater than 20And

Simplifying Perfect Squares

Think about this...

What about larger numbers?

How do you find ?

It helps to know the squares of larger numbers such as the multiples of tens.

102 = 100

202 = 400

302 = 900

402 = 1600

502 = 2500

602 = 3600

702 = 4900

802 = 6400

902 = 8100

1002 = 10000

What pattern do you notice?

For larger numbers, determine between which two multiples of ten the number lies.

102 = 100 1

2 = 1

202 = 400 2

2 = 4

302 = 900 3

2 = 9

402 = 1600 4

2 = 16

502 = 2500 5

2 = 25

602 = 3600 6

2 = 36

702 = 4900 7

2 = 49

802 = 6400 8

2 = 64

902 = 8100 9

2 = 81

1002 = 10000 10

2 = 100

Next, look at the ones digit to determine the ones digit of your square root.

2809

Examples:

Lies between 2500 & 3600 (50 and 60)Ends in nine so square root ends in 3 or 7Try 53 then 57

532 = 2809

Lies between 6400 and 8100 (80 and 90)Ends in 4 so square root ends in 2 or 8Try 82 then 88

822 = 6724 NO!

882 = 7744

7744

15 Find.

16 Find.

17 Find.

18 Find.

19 Find.

20 Find.

21 Find.

22 Find.

23 Find.