Transcript Square roots

PURPOSE
1. Seated and Silent by 7:53.
2. Have forms ready to turn in.
3. Have Student Survey ready to turn in.
4. Complete All About Me Assignment or Time Capsule
Activity if not completed yesterday.
5. All About Me and Time Capsule are on the back counter.
6. Today we will be discussing TCAP scores.
Advisory – Silent
Reading
If you do not
have your own
reading
material, take a
book,
magazine,
comic, or
graphic novel
from my shelf.
Procedures Review
• Think
of at least 3 procedures we
talked about yesterday.
• Be
prepared to share one of those
procedures if your UNO card is drawn.
Square Roots, Cube Roots, and
Irrational Numbers
8.EE.2: Use square root and cube root symbols to represent
solutions to equations of the form x2 = p and x3 = p, where p
is a positive rational number. Evaluate square roots of small
perfect squares and cube roots of small perfect cubes. Know
that √2 is irrational.
Words to know…
•
•
•
•
Square root
Perfect square
Irrational
Cube root
Individual Think Time:
How can you turn two blocks
into a square?
2x2=4
2
2
3x3=9
3
3
4 x 4 = 16
4
4
5 x 5 = 25
5
5
The square root of 4 is
2
The square root of 9 is
3
The square root of 16 is
4
The square root of 25 is
5
Square numbers
Here are the first 10 square numbers:
12 = 1 × 1 = 1
22 = 2 × 2 = 4
32 = 3 × 3 = 9
42 = 4 × 4 = 16
52 = 5 × 5 = 25
62 = 6 × 6 = 36
72 = 7 × 7 = 49
82 = 8 × 8 = 64
92 = 9 × 9 = 81
102 = 10 × 10 = 100
Adding consecutive odd numbers
The tenth
first square
second
third
fourth
fifth
sixth
seventh
eighth
ninth
square
square
square
square
square
square
number
number
number
number
number
number
number
is
isis
isis
1.
25.
is
9.
36.
100.
81.
is16.
64.
4.49.
1+3+
= 54 +
= 79 +
=9
16+
= 11
25 +
= 13
36 +
= 15
49 +
= 17
64 +
= 19
81 = 100
Think about this…..
Could you figure out what the 11th square
number would be?
Think about this…..
What about the 15th square number?
Square roots
Finding the square root is the inverse of finding the square:
squared
8
64
square rooted
We write
64 = 8
The square root of 64 is 8.
Square roots
We can easily find the square root of a square number.
1 = 1
36 = 6
4 = 2
49 = 7
9 = 3
64 = 8
16 = 4
81 = 9
25 = 5
100 = 10
Square numbers
When we multiply a number by itself we say that we are squaring
the number.
To square a number we can write a small 2 after it.
For example, the number 3 multiplied by itself can be written
as
Three squared
3×3
or
32
The value of three squared is 9.
The result of any whole number multiplied by itself is called a
perfect square.
Think about this……
4
?
9
49
?
100
Think about this……
4 2

9 3
49
7

100 10
Approximating Square Roots
Square roots that are not perfect squares are called
irrational. An irrational number in a non-repeating,
non-terminating decimal. This means the decimal
does not repeat, but it also doesn’t end.
Remember
Categorize the following square
roots as rational or irrational.
For example, the 4 is rational because 22 or
2 x 2 = 4. The 5 is irrational because there is
no whole number that can be multiplied by itself
to result in 5.
15
289
160
400
1
Think about this….
• What could be a square root that is
irrational?
• How do you know?
Cubes
5
7
6
8
1
3
2
4
2x2x2=8
2
2
2
3 x 3 x 3 = 27
Cube Roots
The index of a cube root is
always 3.
The cube root of 64 is written as
3
64 .
What does cube root mean?
The cube root of a number is…
…the value when multiplied by itself
three times gives the original number.
Cube Root Vocabulary
radical sign
index
n
x
radicand
Perfect Cubes
If a number is a perfect cube, then
you can find its exact cube root.
A perfect cube is a number that can
be written as the cube (raised to
third power) of another number.
What are Perfect Cubes?
•
•
•
•
•
•
13 = 1 x 1 x 1 = 1
23 = 2 x 2 x 2 = 8
33 = 3 x 3 x 3 = 27
43 = 4 x 4 x 4 = 64
53 = 5 x 5 x 5 = 125
What would the next perfect cube
be?
Examples:
3
64  4
because
 4 4 4    4 
3
 64
Examples:
27  3
3
216  6
3
64  4 
 
125  5 
3
3
3
3
27  3
216  6
64
4

125 5