Square Root Golf!
Estimating Square Roots Numerically
Description
In this activity, you will be using "tiles" to build squares and use the resulting shape to help you identify what
a "Square Root" is and be able to numerically estimate it without a calculator. Once you get the hang of how
to estimate square roots, you will be shooting "Square Root Golf" - a game to test your mastery.
Directions

Place the given amount of "tiles" on your grid paper building a "Large Square".
If all of the tiles are used up, the edge of your square is called the "Square Root" of the number.
4 squares total
Edges of big square - 2

9 squares total
Edges of big square -3
If you have more tiles than it takes to build a large square, then you will “place a proportionately” equivalent piece of each tile
around two adjacent sides of the "large square". To determine the proportionality of these remaining squares, you will divide
the extra tile squares by the total number of border spaces needed to make the next larger square. This process will help you
estimate the Square Root of your number.
7 squares total
3 extra tiles it would take 5 tiles to complete the next size square

Look at the table to help you understand the method
Total Squares Extra Tiles (E) 
Total Border
Used
Spaces (T)
(N)
(divide E by T)
7
3/5
Estimate for Edge
Length
(rounded to the nearest
0.01)
(N)
E/T as a Decimal
0.60
2.60
Calculator Value
for N
(to the nearest 0.01)
2.65

Now, try a few and see how you do. Record your results in the table below:
Worksheet - Rooting Out Square Roots
(Estimates of Various Square Roots)
Total Squares
Used
(N)
Extra Tile
Squares (E)
Total Border
Spaces (T)
(divide E by T)
16
36
6
12
40
5
18
13
20
E/T as a
Decimal
(rounded to the
nearest 0.01)
Estimate for Edge Calculator Value
Length
for 
(to the nearest 0.01)
(
Homework; Let's Go Golfing. . .
Directions for play;
Each foursome will have one die, a calculator and a score card.

One member of the foursome rolls the die twice.
The first roll represents the "Tens" digit of a number and the second roll
represents the "Ones" digit.



Record the number rolled on the score card.
Use the "Square Tiles Method" for estimating the SQUARE ROOT and
record your estimate on the scorecard. [You may NOT use a calculator
at this point, it's +4 stroke penalty]
Square the estimate
A different member of the foursome should use a calculator to do this.

Subtract the "Square of the Estimate" from the Rolled Number
The difference between the original number rolled and the square of the
estimate is you score for that hole.

Add the cumulative score in the final column of your scorecard.
Tee off & Play 9 holes and remember in Golf, the LOWEST score wins.
Square Root Golfing Score Card
Number
Rolled (N)
Square Root
Estimate(
Square of
Estimate
(
Difference of
Squares
Accumulated
Score
Example:
54
54  7.34
(7.34) 
54 - 53.88 =
+0.12
0.12
If you read this far, play a game with mom or dad and record a round of nine holes of golf. You
can get extra credit points. Simply obtain a parent signature on the scorecard, you will get 2 extra
credit points on your next homework grade.