SOLUTION: Read the following lesson estimating square roots. Complete the table at the end and turn in to your instructor.
1. Study the following geometric pattern of squares. What do you
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Question 637154: Read the following lesson estimating square roots. Complete the table at the end and turn in to your instructor.
1. Study the following geometric pattern of squares. What do you notice?
1x1 2x2=4 3x3=9 4x4=16 5x5=25 6x6=36
6x6 + 4 = 40
Did you see that each square in the first row is formed by adding the “L-shaped” piece to the previous smaller square?
2. For 40 tiles, the previous full square contains _______ tiles, making the square that is _____ by ____. The extra 4 tiles are a fractional piece of the “L” that will make the next perfect square. What fraction of the “L-piece” is shaded? ________
We know lies between 6 and 7. Let’s use 4/13 in estimating 6 as an approximate value for . Use this method to complete the table, rounding as shown.
Number Side of
last sq Fractional
L-piece Mixed numeral form Decimal form Sq Root from TI-73 Difference
in values
40 6 4/13 6
6.30769 6.32456 .01687
75
96
125
1x1 2x2=4 3x3=9 4x4=16 5x5=25 6x6=36
6x6 + 4 = 40
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
I assume that the blank spaces should have some pictures, but they did not show up on copying and pasting.
Maybe they looked something like this:
I outlined the squares in different colors, showing the smaller squares on top of the larger one, and marking other tile borders in green.
1) You may notice that each lager square is formed by adding a border, 1 tile wide and L-shaped. That border is made up of two rectangles (an extra horizontal row of tiles and an extra vertical column of tiles) plus a corner square tile.
That tells you that
is the square of the next number, made of
the square of the number, ,
the two rectangles, {2a}}} ,
and the one tile in the corner
You could also notice that as the squares get larger, what is added is a smaller fraction of the original square (and also a smaller fraction compared to the enlarged square.
2) For 40 tiles, the previous full square contains tiles, making the square that is by . The extra 4 tiles are a fractional piece of the “L” that will make the next perfect square. What fraction of the “L-piece” is shaded? .
Adding the fraction to the previous full square side (), you get
(rounded to 5 decimal places)
That is your estimate for .
The calculator says that
(rounded to 5 decimal places)
The difference is
That shows you that your estimate was pretty accurate.
The table you are supposed to fill will show you that as the numbers get larger, the estimates get closer to the calculator result. The estimates get more accurate.
The table should look like this:
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