Transcript How to Find the Square Root of a Non

HOW TO FIND THE SQUARE
ROOT OF A NON-PERFECT
SQUARE
Focus 4 - Learning Goal #2: Students will work with radicals and integer
exponents.
4
3
2
In addition to
level 3.0 and
above and
beyond what
was taught in
class, students
may:
- Make
connection with
other concepts
in math
- Make
connection with
other content
areas.
Students will work
with radicals and
integer exponents.
- Use square root &
cube root symbols to
solve equations in the
form x2 = p and x3 = p.
- Evaluate roots of
small perfect square.
- Evaluate roots of
small cubes.
- Apply square roots
& cube roots as it
relates to volume and
area of cubes and
squares.
Students will be
able to:
- Understand
that taking the
square root &
squaring are
inverse
operations.
- Understand
that taking the
cube root &
cubing are
inverse
operations.
1
With help
from the
teacher, I
have partial
success
with level 2
and 3.
0
Even with help,
students have no
success with the
unit content.
Perfect Squares
• 25, 16 and 81 are called perfect squares.
• This means that if each of these numbers were the area
of a square, the length of one side would be a whole
number.
Area = 81
Area = 25
5
5
4
Area = 16
4
9
9
Perfect Squares
• 12 = 1
• 112 = 121
• 22 = 4
• 122 = 144
• 32 = 9
• 132 = 169
• 42 = 16
• 142 = 196
• 52 = 25
• 152 = 225
• 62 = 36
• 162 = 256
• 72 = 49
• 172 = 289
• 82 = 64
• 182 = 324
• 92 = 81
• 192 = 361
• 102 = 100
• 202 = 400
Non-Perfect Squares
• What about the numbers in between all of the perfect
squares?
• Why isn’t 20 a perfect square?
• 20 can’t make a square with whole numbers. (Area)
1
Area = 20
20
4
2
Area = 20
10
The square root of 20 must be a decimal or
fraction number between 4 and 5.
Area = 20
5
How to find an approximation of the
square root of 20…
What two perfect squares does 20 lie between?
1.
16 and 25
The square root of 16 is 4, so the square root of 20 must be a little
more than 4.
1.
2.
How to find the “little more”
2.
Is the “non-perfect square” 20 closer to 16 or 25?
It seems to be right in the middle. So pick a number in between 4
and 5.
Multiply 4.4 times 4.4. What do you get?
1.
2.
3.
1.
2.
Lets see if we can get closer to 20. Multiply 4.5 times
4.5. What do you get?
4.
1.
2.
5.
19.36
20 – 19.36 = 0.64
20.25
20 – 20.25 = -0.25
4.5 is the best estimate for the square root of 20.
How to find an approximation of the
square root of 150…
1. What two perfect squares does 150 lie between?
1. 144 and 169
2. The square root of 144 is 12, so the square root of 150 must be a
little more than 12.
2. How to find the “little more”
1. Is the “non-perfect square” 150 closer to 144 or 169?
2. It seems to be closer to 144. So pick a number closer to 12.
3. Multiply 12.2 times 12.2. What do you get?
1.
2.
Lets see if we can get closer to 150. Multiply 12.3 times
12.3. What do you get?
4.
1.
2.
5.
148.84
150 – 148.84 = 1.16
151.29
150 – 151.29 = -1.29
12.2 is the best estimate for the square root of 150.
How to find an approximation of the
square root of 200…
1. What two perfect squares does 200 lie between?
1. 196 and 225
2. The square root of 196 is 14, so the square root of 200 must be a
little more than 14.
2. How to find the “little more”
1. Is the “non-perfect square” 200 closer to 196 or 225?
2. It seems to be really close to 196. So pick a number close to 14.
3. Multiply 14.1 times 14.1. What do you get?
1.
2.
Lets see if we can get closer to 200. Multiply 14.2 times
14.2. What do you get?
4.
1.
2.
5.
198.81
200 – 198.81 = 1.19
201.64
200 – 201.64 = -1.64
14.1 is the best estimate for the square root of 200.