 # Squares, Square Roots and Perfect Squares

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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...

Click to see if the answer found with the Area formula is correct!
Area of a Square The area (A) of a square can be found by squaring its side length, as shown below: A = s2 Click to see if the answer found with the Area formula is correct! A = 42 = 4 4 = 16 sq.units The area (A) of a square is labeled as square units, or units2, because you cover the figure with squares... 4 units

What is the area of a square with sides of 5 inches?
1 What is the area of a square with sides of 5 inches? A 16 in2 B 20 in2 C 25 in2 D 30 in2 Answer: C

What is the area of a square with sides of 6 inches?
2 What is the area of a square with sides of 6 inches? A 16 in2 B 20 in2 C 24 in2 D 36 in2 Answer: D

If a square has an area of 9 ft2, what is the length of a side?
3 If a square has an area of 9 ft2, what is the length of a side? A 2 ft B 2.25 ft C 3 ft D 4.5 ft Answer: C

What is the area of a square with a side length of 16 in?
4 What is the area of a square with a side length of 16 in? Answer: 256 sq in

What is the side length of a square with an area of 196 square feet?
5 What is the side length of a square with an area of 196 square feet? Answer: 14 ft

When you square a number you multiply it by itself.
52 = = 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 3 (and so on)

Number Square 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 1 2 4 3 9 4 16 5 25 6 36 7 49 8 64 9 81 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 = 9 What is 169?

Square Perfect Root Square 1 1 2 4 3 9 4 16 5 25 6 36 7 49 8 64 9 81 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 Answer: 1

7 What is ? 81 Answer: 9

8 What is the square of 15 ? Answer: 225

9 What is ? 256 Answer: 16

10 What is 132? Answer: 169

11 What is ? 196 Answer: 14

12 What is the square of 18? Answer: 324

13 What is 11 squared? Answer: 121

14 What is 20 squared? Answer: 400

Squares of Numbers Greater than 20 Simplifying Perfect Squares
Day 13 Squares of Numbers Greater than 20 And Simplifying Perfect Squares

What pattern do you notice?
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? Teacher Instructions: Number in tens place squared, then two zeros are added

For larger numbers, determine between which two multiples of ten the number lies.
102 = = 1 202 = = 4 302 = = 9 402 = = 16 502 = = 25 602 = = 36 702 = = 49 802 = = 64 902 = = 81 1002 = = 100 Next, look at the ones digit to determine the ones digit of your square root.

Ends in nine so square root ends in 3 or 7 Try 53 then 57 532 = 2809
Examples: Lies between 2500 & 3600 (50 and 60) Ends in nine so square root ends in 3 or 7 Try 53 then 57 532 = 2809 Lies between 6400 and 8100 (80 and 90) Ends in 4 so square root ends in 2 or 8 Try 82 then 88 822 = NO! 882 = 7744 2809 7744 Teacher Instructions: List of Squares 102 = = 1 202 = = 4 302 = = 9 402 = = 16 502 = = 25 602 = = 36 702 = = 49 802 = = 64 902 = = 81 1002 = = 100

15 Find. Answer: 28 Teacher Instructions: List of Squares
102 = = 1 202 = = 4 302 = = 9 402 = = 16 502 = = 25 602 = = 36 702 = = 49 802 = = 64 902 = = 81 1002 = = 100

16 Find. Answer: 42 Teacher Instructions: List of Squares
102 = = 1 202 = = 4 302 = = 9 402 = = 16 502 = = 25 602 = = 36 702 = = 49 802 = = 64 902 = = 81 1002 = = 100 42

17 Find. Answer: 65 Teacher Instructions: List of Squares
102 = = 1 202 = = 4 302 = = 9 402 = = 16 502 = = 25 602 = = 36 702 = = 49 802 = = 64 902 = = 81 1002 = = 100

18 Find. Answer: 48 Teacher Instructions: List of Squares
102 = = 1 202 = = 4 302 = = 9 402 = = 16 502 = = 25 602 = = 36 702 = = 49 802 = = 64 902 = = 81 1002 = = 100

19 Find. Answer: 79 Teacher Instructions: List of Squares
102 = = 1 202 = = 4 302 = = 9 402 = = 16 502 = = 25 602 = = 36 702 = = 49 802 = = 64 902 = = 81 1002 = = 100

20 Find. Answer: 99 Teacher Instructions: List of Squares
102 = = 1 202 = = 4 302 = = 9 402 = = 16 502 = = 25 602 = = 36 702 = = 49 802 = = 64 902 = = 81 1002 = = 100

21 Find. Answer: 59 Teacher Instructions: List of Squares
102 = = 1 202 = = 4 302 = = 9 402 = = 16 502 = = 25 602 = = 36 702 = = 49 802 = = 64 902 = = 81 1002 = = 100

22 Find. Answer: 47 Teacher Instructions: List of Squares
102 = = 1 202 = = 4 302 = = 9 402 = = 16 502 = = 25 602 = = 36 702 = = 49 802 = = 64 902 = = 81 1002 = = 100

23 Find. Answer: 101 Teacher Instructions: List of Squares
102 = = 1 202 = = 4 302 = = 9 402 = = 16 502 = = 25 602 = = 36 702 = = 49 802 = = 64 902 = = 81 1002 = = 100