Estimating and approximating
square root notes
Absent copy
Thurs/Fri 3/13,14
Four steps to approximating square roots
Step 1: Find the two sq. roots (perfect squares) that lie below and
above the non-perfect square. Then estimate(educated guess) what
you think the answer will be.
Below
Above
16
9
11 ____
Ex:
____
What is your estimation of what the sq. root of 11 will be?
The square root is closer to
9
so pick something like 3.2. Since the 9 is 3 that is a good guess.
Step 2: Divide the radicand (11) by the estimation you came up with
and get a quotient (answer).
3.4
11 =
3.2 11
3.2
Step 3: Take the average by adding your (estimate + quotient)
3.2 + 3.4 = 6.6
2
2
2
Step 4: round your answer to the 10ths place.
3.30
Example
1
• Is this square root a perfect
• Approximate to the 10ths
place (use principal root).
14
below
above
9
16
Estimation:
Its closer to 16 so 3.7 might be a good
answer.
Divide:
14
3.7
=
3.8
Average:
3.7 + 3.8 = 7.5 = 3.75
2
2
Round to 10th place.
3.75 the 7 is in the 10th place the 5
will round the answer to 3.8
3.8
Solution
square?
YES or NO
• What is the radicand?
•
The radicand is 14
•
It lies between the
•
It is closer to the
•
You divide the radicand by you estimate you
made.
• Step 1: What 2 perfect square
does 14 lie between.
9 and
16
• Is it closer to √9 or √16. Make a
educated guess (estimate) on
what you think the answer will be.
16
so 3.7 might be good.
• Step 2: What 2 #’s do I divide to
get the quotient?
• Step 3: How do you get the
average after you add your
estimate and the quotient?
•
You divide by 2 to get your average.
•
You round to the nearest 10ths place.
• Step 4: What place value do we
round the answer too?
Example 2
Approximate to the 10ths • Is this square root a perfect square?
YES or NO
place (use principal root).
• What is the radicand?
below
16
Estimation:
22
above
25
Its closer to 25 so 4.7 might be
good answer for the sq. rt. of 22.
•
The radicand is 22
•
It lies between the
•
It is closer to the
• Step 1: What 2 perfect square does
between.
•
22 = 4.7
4.7
•
Average: 4.7 + 4.7 = 9.4 4.70
•
2
2
Round to 10th place.
4.7
Solution
25
• Is it closer to √16 or √25. Make a educated
guess (estimate) on what you think the answe
will be.
Divide:
4.70 the 7 is in the 10th place the 0
will keep the 7 in the 10ths place.
16 and
22 lie
25
so 4.7 might be good.
Step 2: What 2 #’s do I divide to get the
quotient?
You divide the radicand by you estimate you made.
Step 3: How do you get the average after yo
add your estimate and the quotient?
•
You divide by 2 to get your average.
•
You round to the nearest 10ths place.
• Step 4: What place value do we round the
answer too?