1. Squares and Square Roots

2. Vocabulary
Square root
Perfect square
Radical sign
Irrational numbers

3. Guiding Questions How would you define “square root”?
When will a square root be a whole number? When will it be irrational?
Can a square root be a decimal as 2.25? Explain
What connection can be made between the side length of a square and the area of the square?
If a square as an area of 100, what is the perimeter?

4. By definition Ö25 is the number you would multiply times itself to get 25 for an answer.
Because we are familiar with multiplication, we know that Ö25 = 5
Numbers like 25, which have whole numbers for their square roots, are called perfect squares
You need to memorize at least the first 15 perfect squares

5. Perfect square
Square root
Perfect square
Square root 1
Ö1 = 1 81
Ö81 = 9 4
Ö4 = 2
100
Ö100 = 10 9
Ö9 = 3
121
Ö121 = 11 16
Ö16 = 4
144
Ö144 = 12 25
Ö25 = 5
169
Ö169 = 13 36
Ö36 = 6
196
Ö196 = 14 49
Ö49 = 7
225
Ö225 = 15 64
Ö64 = 8

6. Every whole number has a square root
Most numbers are not perfect squares, and so their square roots are not whole numbers.
Most numbers that are not perfect squares have square roots that are irrational numbers
Irrational numbers can be represented by decimals that do not terminate and do not repeat
The decimal approximations of whole numbers can be determined using a calculator

7. Obj: To find the square root of a number
Find the square roots of the given numbers
If the number is not a perfect square, use a calculator to find the answer correct to the nearest thousandth. 81
Ö81 = 9 37
Ö37 »
158
Ö158 »

8. Obj: To find the square root of a number
Find two consecutive whole numbers that the given square root is between
Try to do this without using the table
Ö16 = 4 and Ö25 = 5 so
Ö18
Ö18 is between 4 and 5
Ö115
Ö100 = 10 and Ö121 = so
Ö115 is between 10 and 11

9. Obj: To find the square root of a number
Square and square root are inverse operations (they undo each other)
Find the length of a square by using inverse operations
Area = 36 units2

10. A square window has an area of 169 square inches
A square window has an area of 169 square inches. How wide is the window?

11. A square shaped kitchen table has an area of 16 square feet
A square shaped kitchen table has an area of 16 square feet. Will it fit through a van door that has a 5 foot wide opening?

12. A square window has an area of 169 square inches
A square window has an area of 169 square inches. What is the perimeter of the window?

13. Guiding Questions (you should be able to answer)
How would you define “square root”?
When will a square root be a whole number? When will it be irrational?
Can a square root be a decimal as 2.25? Explain
What connection can be made between the side length of a square and the area of the square?
If a square as an area of 100, what is the perimeter?

14. Multiplying radicals
The product of the square roots of two numbers is the same as the square root of the product of the numbers
Examples: Ö3
Ö12 =
Ö36 Ö7
Ö11 =
Ö77

15. Simplify the following expressions
-Ö4 = -2
7Ö64 + 9 = =
56 + 9
= 65
Ö25
Ö49 = =
25 + 7
= 32

16. Ö Ö Ö Simplify the following expressions = = 1 1 – = – 6 12 2 1 = – 124 Ö4 2 = = 81
Ö81 9 1 1 Ö 1 Ö 1 – = – 36 6 12
144 2 1 = – 12 12 1 = 12

17. Simplified radical form
No factor inside the radical should be a perfect square.
Ö18 =
Ö9 2 = Ö9 Ö2 = 3 Ö2
Ö108 =
Ö36 3 =
Ö36 Ö3 = 6 Ö3
Ö96 =
Ö16 6 =
Ö16 Ö6 = 4 Ö6