Transcript Square Roots

Essential Question
How do you find the roots of perfect squares
and cubes?
706.2.3
Square Roots
• What do you think of when you hear the
word square?
• Now get shapes out of your head and
think numbers.
Activator
• Any # times itself is called what?
• Any # times itself 3 times is called what?
Square Roots
Squares
Cubes
Squares and Square Roots
• This lesson is divided into two parts, the
numbers and their roots.
• A whole number can be referred to as a
square: Meaning that you can multiply the
same number by itself to achieve the
whole number: Example: 4 is a square,
because 2 x 2 = 4
Squares and Square Roots
• The number that you multiply by itself to get the whole
number is the square root. So 2 is the square root of
4.
• Not every whole number has a perfect square root,
meaning that not every number has a whole number
that can be multiplied by itself to get the square.
Example: 2 does not have a perfect square root.
1. 4142135623… x 1.4142135623…= 2
Squares and Square Roots
• The numbers that do not have perfect
square roots have irrational square roots.
• √ this symbol is called a radical: The
number under the radical is called the
radicand. √7 so 7 is the radicand and √ is
the radical.
Square Root
Radicand: #
under the radical
√8
Radical or
root symbol
Practice
• √36
• √49
• √144
• √169
Cube Root
This is the index #. It
tells how many times
you would multiply the
root by to get the
radicand
Radicand: #
under the radical
√8
3
Radical or
root symbol
Squares and Square Roots
• √ this is the symbol for root: When you see
this before a number: √4 it is asking for the
number that can be multiplied by itself to
form the number inside.
• The √ usually does not have an index of 2
when asking for the square root, but with
other roots you will see a tiny number above
the radical to indicate what type of root you
are looking for.
• Examples: 2√8 or √8 both mean square root,
but
• 3√9 means the cube root or what times itself 3
times will equal 9
Practice
• 3√27
• 3√8
• 3√64
• 3√1000
Assessment Prompt
• What is the difference between a square
root and a cube root?
• How many roots does a number have?
• What is the positive square root called?
Radical Race
1. Start with the square root of 9
2. Next person add 13 to the answer above
3. Next person find the square root to the
answer of #2
4. Next person multiply the answer to #3 by
16
5. Next person find the square root to #4
answer
Hold up your answer when your group is
finished
Essential Question
How do you compare and order roots?
706.2.9:Compare and order rational
numbers and roots of perfect
squares/cubes; determine their
approximate locations on a number line.
• Pass out copy of perfect squares and
square roots.
Approximating Square and Cube
Roots
• To approximate a root find the two perfect
roots the number would fall between:
• Ex: √74 is between the √64 and √81
• Which is closer to √74? What is the square
root?
Guided Practice
• √18
• √88
• √110
Ordering and Comparing Roots
• Convert the square roots to their actual
value: √81 and √100
• Hint, the larger radicand will always have
the larger root.
• Place the following square roots on a number
line √16, √36, √4, √42 , √64
Assessment Prompt
• What are perfect squares and cubes?
• Is an approximation the exact square root?
Writing Prompt
• Letter to an absent student:
• Explain how to approximate the square
root of the following number: √72 to a
student who is absent. (Even there are no
absent students you still write the letter.
Address it to Dear Absent Student, )
Tic-Tac-Think:
Square/cube roots
Choose one task from each column to answer completely.
Find the root:
√36
Find the root:
√64
Find the root:
3√64
Between which two
roots would the
root of the following
fall.
√27
Between which two
roots would the
root of the following
fall.
√58
Between which two
roots would the
root of the following
fall.
√ 76
Using your answer
in the second
column, which
perfect root is your
answer closest?
Using your answer
in the second
column, which
perfect root is your
answer closest?
Using your answer
in the second
column, which
perfect root is your
answer closest?
Essential Question
How do you determine when a square root
is irrational?
706.2.10: Recognize when a whole number
is not a perfect square, then its square
root is not rational and cannot be written
as the ratio of two integers.
Recognizing when a square root is
irrational.
• Activator:
• What are irrational numbers?
• Write the prime factorization of 84 (use a
factor tree)
Factor Trees
√36
3
12
6 (Perfect square)
Factor Trees
√48
6
2
8
3 2
2
2 * 2 √3 =
4
2
4√3 (Not Perfect)
Factor Trees
√64
8
8
8 (Perfect square)
Practice:
• √25
• √49
• √28
Cube Roots
• √27 What number can you multiply
itself 3 times will equal 27
3
27
9
3
3
3
Practice
√64
3
3
√8
3
√120
• In your own words, how do you determine
when a square root is irrational?
• Do you have to factor out every square
root to determine this?
3-2-1
• Determine if the following three square
roots are rational or irrational: √15, √49,
√33
• Tell between which two roots the root of
√42 would fall.
• Answer the EQ?