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Chapter 8 Lesson 1
Roots and Square Roots
What is a square root
and how do you solve it?
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for correct lettering.
Square Roots
This should be easy.
Squares are my favorite shape.
Do your squares have roots?
Sure, then they grow
into square trees.
Ok, for real. What does
a root do for a plant?
Root is where the plant starts.
Square roots do the
same thing for a number.
I'll get a square to show you.
4 square feet
? ft
?
ft
This square has 4 square feet.
How long is each side?
4 square feet
2 ft
2 ft
Each side is 2 feet long.
Just multiply them to get 4 sq ft.
2 ft
4
2 ft
Square root uses the area
of a square to find square root.
That's where the number starts.
2 ft
4
2 ft
Do I have to draw squares
to make square roots?
2 ft
4
2 ft
There is a sign it uses.
Here's what it looks like.
4
This is the square root of 4.
4
It looks like
a division sign to me.
4
Can I think like it's division?
4
You're right, but it shows
square root.
2
2
4
If it was, then
it would look like this.
2
2
4
That looks kind of strange.
How do you really write it?
4 =2
That's why we write it like this.
4 =2
Do you multiply
or divide to solve these?
Multiply or Divide
Either one is fine.
Here's a problem for multiplication.
9
What number multiplies
by itself to get 9?
9=3
That would be 3 x 3 = 9.
Am I right?
Multiply
3x3=9
Exactly right.
Square root multiplies
the same 2 numbers.
Division does the same thing.
Divide
9
3=3
It's like going backwards.
9 =3
Either way you find it,
the answer is the same.
Ok, another problem.
25
How do you multiply to
find the square root of 25?
5 x 5 = 25
Multiply same numbers.
That means 5 times 5 is 25.
Division does the same thing.
25
5=5
25 divided by 5.
5th grade math, for sure.
25 = 5
Either way you find it,
the square root of 25 is 5.
I'll make a bunch of problems.
16
49
81
Is that the toughest you got?
I know all of those.
16
49
81
4x4
7x7
9x9
See? It's all the doubles.
Is that the toughest one you've got?
2500
How about the
square root of 2500?
Is that tough enough for you?
2500
Ok, that is alot tougher.
How do you find it?
2500 = 50
50? That means
50 times 50 makes 2500.
2500 = 50
You are exactly right.
50 x 50 = 2500
There's 1 more way
you can write square roots.
25
=
25
?
You can write a square
root with an exponent.
You'll never guess what it is.
25 = 25
1
2
The exponent for
square root is 1 half.
I knew you'd never get it.
25 = 25
1
2
Half? 1 half makes a square
root? That looks really weird.
25
1
2
=
5
Chill out. It's just another
way of writing square root.
I'll go over 1 more thing.
Radical
Radical is another name for a root.
Radical
Root? What happened
to the square part?
Radical
Root
You know, there's more
kinds of roots than square roots.
I can tell. This is going
to be a very long chapter.
Qs
Where do they
get square roots from?
2 ft
4
square feet
2 ft
Square roots use squares.
The sides are multiplied like area.
64
Name 2 ways to find the
square root of 64.
8 x 8 = 64
Multiply same numbers.
64
8=8
Divide same numbers.
36
What is the
exponent for square roots?
36
=
36
1
2
1 half.
Roots use fraction exponents.
Lesson #1
Variable
Multiply
Variables
Any number
goes in one.
3 ways to
multiply a variable.
Chapter 8 Lesson 1a
Roots and Square Roots
What is a cube root
and how do you solve it?
Roots
Are these other roots
different from square roots?
In most ways they are the same.
Here's one we use alot.
Hey, it's a box.
Got any presents in there?
This just isn't any box.
Wait until you see how it's different.
It looks like a box.
Smells like a box. Must be a box.
It is a certain kind of a box
with a certain kind of name.
Cube
Oh yeah, we studied
cubes when we did geometry.
Cube
How is it like a square?
Equal Sides
2 ft
2 ft
They both have equal sides.
Does it have a root?
2 ft
cube root
3
8
It's called a cube root
and it has a 3 in the root sign.
What 3 same numbers multiply to 8?
2x2x2=8
I know 2 x 2 x 2 makes 8.
What's another cube root?
3x3x3
It's easier to start cube
roots with what multiplies.
What will this cube root be?
3
27
It has to be 3 x 3 x 3 is 27.
Wow. These roots go up fast.
8
27
3x3x3
4x4x4
Got that right.
What does the cube of 4 find?
3
64
Sure, we did 4 x 16 before.
Let me see all 3 cubes.
8
27
64
3x3x3
4x4x4
Like I said, cubes go
up very quickly.
You definitely know the next one.
3
125 = 5
Easy to remember, five 25s.
3
125 = 5
We use the 5s one alot.
I don't think you
remember the next one.
3
216 = 6
216? Never seen it before.
Do I have to know these?
3
?
=7
7x7x7
Not really, but
I like to go over them.
You know 7 x 7 is 49. Estimate 7.
3
343 = 7
7 x 50 is 350. Take away 7.
I don't even know 8 and 9.
3
3
512 = 8
729 = 9
The 9 fact is easier than 8.
There is 1 cube root left.
3
1000 = 10
Square root of 100 is 10,
so cube root is 1000.
Is that all I have to know?
3
27 = 27
?
The fraction exponent for
square root was 1 half.
What do you think cube root is?
3
27
=
27
1
3
Cube root has to have
1 third as an exponent.
Woe, we learned alot this lesson.
Roots
Yesterday I thought square
roots made square trees.
And now we're talking about
radicals and cube roots.
I liked those square trees.
I know. All my trees in art
looked like square trees.
Qs
3
8
How do you solve a cube root?
3
8
Multiply the same
number 3 times.
2x2x2=8
5
3
What shape uses cube roots?
5
3
5 ft
5 ft
5 ft
Cube roots come from cubes.
2
5
What is the cube of 2 and 5?
5x5x5
2x2x2
3
8
3
125
Cube root of 8 is 2 and 125 is 5.
3
27
What is the exponent
for cube roots?
27
=
27
1 Third
1 third is the exponent
fraction for cube root.
1
3
Chapter 8 Lesson 1
Roots and Square Roots
Short Lesson
What is a square root
and how do you solve it?
A root is
where a plant starts.
How does that
work with numbers?
Square Root
How does a square start a number?
2 ft
4
2 ft
Square root uses the area
of a square to find square root.
We have a sign for it.
4
Square root of 4.
It looks like a division sign,
but it's a square root sign.
Here's 1 way to solve it.
2x2=4
Multiply same
numbers to get 4.
There's another way to find it.
9
3=3
Divide with
same numbers.
There is a sign that shows square root.
9 =3
Looks like a division sign.
What's the exponent for square root?
25
=
25
1
2
=
The exponent for
square root is 1 half.
You'll need to know
the perfect square roots.
5
64
121
144
These are perfect square roots
Solve them.
64
121
144
8
11
12
A perfect root has a
whole number answer.
What kind of a box is this?
Cube has
Equal Sides
2 ft
2 ft
Just like square did.
What's the cube with 2?
2 ft
3
8 =2
The cube root of 8 is 2.
What cube root equals 3?
3
27 = 3
3 x 3 x 3 is 27
Cube root of 27 is 3.
Cube root has an exponent, too.
27
1
3
=
3
Cube root
exponent is 1 third.
Questions
64
How do you multiply to
find the square root of 64?
8 x 8 = 64
Multiply same 2 numbers.
64
=
8
Square root is 8
36
What is the exponent
for a square root?
36 = 36
1
2
Exponent for
square root is 1 half.
How is a cube root different
from square root?
3
8
2x2x2=8
Multiply 3 same numbers.
What is the exponent?
3
8 =2
1
3
Exponent for
cube root is 1 third.
Chapter 8 Lesson 1
Roots and Square Roots
Practice #1
What is a square root
and how do you solve it?
Where do they
get square roots from?
2 ft
4
square feet
2 ft
Square roots use squares.
The sides are multiplied like area.
64
Name 2 ways to find the
square root of 64.
8 x 8 = 64
Multiply same numbers.
64
8=8
Divide same numbers.
3
8
How do you find a cube root?
3
8
2x2x2=8
Cube multiplies
3 same numbers.
9
3
8
What are the exponents for
square and cube roots?
3
9
9
1
2
8
8
1
3
1 Half and 1 Third
Problems
36
How do you solve a square root?
36 = 6
Multiply same numbers.
6 x 6 = 36
Square root of 36 is 6.
49
Solve the square root of 49.
49
7x7
7
Square root of 49 is 7.
121
What's the square root of 121?
121
11 x 11
11
Square root of 121 is 11.
3
27
What's the cube root of 27?
3
27
3x3x3
3
Cube root of 27 is 3.
Chapter 8 Lesson 1
Roots and Square Roots
Practice #2
What is a square root
and how do you solve it?
Where do they
get square roots from?
2 ft
4
square feet
2 ft
Square roots use squares.
The sides are multiplied like area.
64
Name 2 ways to find the
square root of 64.
8 x 8 = 64
Multiply same numbers.
64
8=8
Divide same numbers.
3
8
How do you find a cube root?
3
8
2x2x2=8
Cube multiplies
3 same numbers.
9
3
8
What are the exponents for
square and cube roots?
3
9
9
1
2
8
8
1
3
1 Half and 1 Third
Problems
196
What's the square root of 196?
196 = 14
Square root of 196 is 14.
256
What's the square root of 256?
256 = 16
Square root of 256 is 16.
400
What's the square root of 400?
400 = 40
Square root of 400 is 40.
3
125
What's the cube root of 125?
3
125
3x3x3
5
Cube root of 125 is 5.
Chapter 8 Lesson 1
Roots and Square Roots
Performance #1
What is a square root
and how do you solve it?
25
81
Find these roots.
25 = 5
81 = 9
36
121
Find these roots.
36 = 6
121 = 11
169
400
Solve the roots.
169 = 13
400 = 20
196
900
Solve the roots.
196 = 14
900 = 30
3
27
3
8
Solve the cube roots.
3
64 = 4
3
8=2
2
64
3
64
Why is 64 different?
2
64 = 8
3
64 = 4
It's both a square and cube root.
Chapter 8 Lesson 1
Roots and Square Roots
Performance #2
What is a square root
and how do you solve it?
16
49
Find these roots.
16 = 4
49 = 7
64
144
Find these roots.
64 = 8
144 = 12
225
256
Solve the roots.
225 = 15
256 = 16
625
1600
Solve the roots.
625 = 15
1600 = 40
2
81
4
81
Why is 81 different why?
2
81 = 9
4
81 = 3
The quad root is 3.
Square root is 9.
3
125
3
216
What's the cube root
of 125 and 216?
3
125 = 5
3
216 = 6
125 is 5 and 216 is 6.