from square numbers to square roots (lesson 2)
DESCRIPTION
Students will use their understanding of square numbers to evaluate square roots. Remember, square roots, quite literally mean going from square numbers, back to the root - the number which you multiplied in the first place to get the square number. Example: The square root of 49 is 7.TRANSCRIPT
From Square Numbers to Square Roots
Grade 8 MathematicsMr. J. Lingley
Square # ReviewThese numbers below are not square numbers. Which two consecutive square numbers is each number between?
12
40
75
200
How do you know?
Square # ReviewThe floor of a large square room has an area of 144 m2. What is the length of a side of the room? How much baseboard is needed to go around the room?
Square # ReviewThe floor of a large square room has an area of 144 m2. What is the length of a side of the room? How much baseboard is needed to go around the room?
Is there a shorter way to find the side length?
144
144What th
e
heck is that
?
Square RootsThe square root ( ) of a number finds the factor that when multiplied by itself will give you the square number. In other words it goes from area to side length. Back to the root.
144 = 12 122 = 144A square root and a square are opposite operations.
Even donald knows something about square roots.
Exploring Square Roots
Fun With Squares and Square roots!
Name: Date: ! ! ! ! Class:
In class we have been observing that any whole number multiplied by itself will give us a square number. Now it’s time to look at what the factors of those square numbers tell us. Factor: A number that divides exactly into another number. For example, 1,2,3 and 6 are factors of 6.
What are all of the factors of 10?
Please help!
Investigate!
Working with a partner, complete the table below. Indicate all of the factors for a given whole number along the bottom of the table. Remember, that if a number multiplied by itself gives you the target whole number, only copy down that factor once. For instance: 9 = 3 x 3, however the factors for 9 are: 1, 3, 9 - not 1, 3, 3, 9.
6 8
4 3 4
2 3 2 5 2 7 2
1 1 1 1 1 1 1 1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
start here!
Questions:
1. Which numbers have only two factors? What do you notice about these numbers?
2. Which numbers have an even number of factors, but more than 2 factors?
3. Which numbers have an odd number of factors?
Exploring Square Roots
Fun With Squares and Square roots!
Name: Date: ! ! ! ! Class:
In class we have been observing that any whole number multiplied by itself will give us a square number. Now it’s time to look at what the factors of those square numbers tell us. Factor: A number that divides exactly into another number. For example, 1,2,3 and 6 are factors of 6.
What are all of the factors of 10?
Please help!
Investigate!
Working with a partner, complete the table below. Indicate all of the factors for a given whole number along the bottom of the table. Remember, that if a number multiplied by itself gives you the target whole number, only copy down that factor once. For instance: 9 = 3 x 3, however the factors for 9 are: 1, 3, 9 - not 1, 3, 3, 9.
6 8
4 3 4
2 3 2 5 2 7 2
1 1 1 1 1 1 1 1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
start here!
Questions:
1. Which numbers have only two factors? What do you notice about these numbers?
2. Which numbers have an even number of factors, but more than 2 factors?
3. Which numbers have an odd number of factors?
Calculators are permitted.
Fun With Squares and Square roots!
Name: Date: ! ! ! ! Class:
In class we have been observing that any whole number multiplied by itself will give us a square number. Now it’s time to look at what the factors of those square numbers tell us. Factor: A number that divides exactly into another number. For example, 1,2,3 and 6 are factors of 6.
What are all of the factors of 10?
Please help!
Investigate!
Working with a partner, complete the table below. Indicate all of the factors for a given whole number along the bottom of the table. Remember, that if a number multiplied by itself gives you the target whole number, only copy down that factor once. For instance: 9 = 3 x 3, however the factors for 9 are: 1, 3, 9 - not 1, 3, 3, 9.
6 8
4 3 4
2 3 2 5 2 7 2
1 1 1 1 1 1 1 1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
start here!
Questions:
1. Which numbers have only two factors? What do you notice about these numbers?
2. Which numbers have an even number of factors, but more than 2 factors?
3. Which numbers have an odd number of factors?
Odd # of Factors Even # of Factors
Odd # of Factors Even # of Factors
square number
When a number has an odd number of factors, it is a square
number.
36 = 1, 2, 3, 4, 6, 9, 12, 18, 36 9 Factors
The square number can be always found in the middle.
Fill in this table...
Square Root Square Number
4
64
144
7
13
100
Your Turn1. The factors of 136 are listed in ascending order. 136 = 1, 2, 4, 8, 17, 34, 68, 136Is 136 a square number?
2. Find:
25 64 81
162
42 62 82 72 92 12