Finding Square Roots &
Cube Roots
Lesson 1.1 part 3
Squares and Square Roots
52 = ?
25
√25 = ?
5
82 = ?
64
√64 = ?
8
122 = ?
144
√144 = ? 12
Notice that they are Inverses of each other!
Square Roots have TWO answers
x2 = 196
What
number
make 196
when
multiplied
by itself?
√196 = ?
+
14
BOTH positive &
negative answer
make 196 so…
Square Roots with Fractions
x2
=
9
256
What number
make 9 when
multiplied,
then what
makes 256?
3
√9 = ?
√256 = ?
+
16
3
16
BOTH positive &
negative answer
make 9 & 256
so…
Cube Roots are a little different…
x3 = 512
What number
makes 512
when
multiplied by
itself THREE
times???
8 x 8 = 64
√512 = ? 64 x 8 = 512
Put a little 3
= 8
in the
corner of
BUT…only the
the square
POSITIVE
root box!
version…
3
-8 x (-8) = 64
64 x (-8) =
-512
Cube Roots with Fractions
x3 = 64
343
Remember to
multiply a
number
THREE times!
4 x 4 = 16
√64 = ? 16 x 4 = 64
3
3
7 x 7 = 49
49 x 7 = 343
√343 = ?
4
7
Again…only the
POSITIVE
answers work!!!
Lets Practice!
x2 = 9
49
x3
= 216
+
3
7
x2 = 324
+
6
x3 = 8
125
2
5
18
Lets Practice!
x3
= 3,375
x2 = 25
169
15
+
5
13
x2 = 1
+
x3 = 64
343
4
7
1
Estimating Square Roots
√6 ≈ ?
√9 = 3
No number
makes 6 when
squared…it is
an
IRRATIONAL
number!
√4 = 2
Find a
Perfect
Square that
is larger and
smaller than
6!
So the answer must be
BETWEEN these two!
= 2.5
If right in the middle .5
If closer to small number .2
If closer to big number .8
We could estimate it even more if
necessary!
We could
estimate it
even more if
necessary
√6 ≈ 2.5
Choose some
numbers
between 2 &
3 and square
them!
2.4 = ? = 5.76
2.5 = ? = 6.25
2.6 = ? = 6.76
Now, which answers is
6.0 between????
√6 ≈ 2.45
Since it falls between 2.4 and
2.5 do 2.45
(its between the two!!!)
It gets easier…I PROMISE!!!!
√10 ≈ ?
No number
makes 10
when
squared…it is
an
IRRATIONAL
number!
√16 = 4
√9 = 3
Find a
Perfect
Square that
is larger and
smaller than
6!
So the answer must be
BETWEEN these two!
= 3.2
Since 10 is
pretty much
closer to 9
use
something
like 3.2
instead
Lets go TWO decimal places now!
√10 ≈ 3.2
Choose some
numbers
between 3 &
4 and square
them! But
stick closer
to 3!
3.1 = ? 9.61
3.2 = ? 10.24
3.3 = ? I found my answer
already!
√10 ≈ 3.15
Since it falls between 3.1 and
3.2 do 3.15
(its between the two!!!)
Practice…
√21 ≈ ?
√25 = 5
√16 = 4
= 4.5
4.4 = ?
19.36
4.5 = ?
20.25
4.6 = ?
Now find one more
decimal place!
√21 ≈ 4.55
Practice…
√2 ≈ ?
√4 = 2
√1 = 1
= 1.5
1.4 = ?
1.96
1.5 = ?
2.25
1.6 = ?
Now find one more
decimal place!
√2 ≈ 1.45
Practice…
√15 ≈ ?
√16 = 4
√9
= 3
= 3.8
3.7 = ?
13.69
3.8 = ?
14.44
3.9 = ?
15.21
Now find one more
decimal place!
√15 ≈ 3.85