learning goal: identify the two consecutive whole numbers between which the square root of a...
TRANSCRIPT
Learning Goal:
Identify the two consecutive whole numbers
between which the square root
of a non-perfect square whole number
less than 225 lies
(with and without the use of a number line)
Perfect Squares (a review)
1) 25 2)
49144
1169 3)
4) 5) 6)
4900
196100
162254
36
900
7) 8) 9)
10) 11) 12)
13) 14) 15)1600
64
14400400
81
121
9
16) 17) 18)
1000019) 20) 21)
Perfect Squares (a review)Answers
1) 25 55 2)
49144
1169 1313 3) 11
4) 1212 5) 77 6) 3030
4900
196100
162254
36
900
7) 22 8) 1515 9) 44
10) 1010 11) 66 12) 1414
13) 7070 14) 33 15) 881600
64
14400400
81
121
9
16) 1111
17) 4040 18) 2020
1000019) 99 20) 120120 21) 100100
Non-Perfect SquaresHere is the list of perfect squares perfect squares from 1 to 256.
11
24
39
416
525
636
749
864
981
10100
11121
12144
13169
14196
15225
16256
Not every number is a perfect square.
If they aren’t, we call them non-perfect squaresnon-perfect squares.
To find the square root of a number that is not a perfect square, we use estimation with perfect squares.
Non-Perfect Squares
Using the above information (which we should have memorized), what two numbers would the answer to be between?
Using dot paper try to make a perfect square out of 10 squares. Can you do it?
There is an answer to the square root of 10. We just have to use what we know about the
perfect squares to find it.
11 24 39 416 525
10
Since 10 is between 9 and 16, the answer to is between the answer to and the answer to .
16910
Non-Perfect Squares
39 416
Since 10 is between 9 and 16, and the answers for those square roots are 3 and 4, the square root of 10 would be between 3 and 4… probably closer to 3 because 10 is closer to 9 than 16. It would be plotted on a number line as below.
10
9 1610
3 43.53.162277
…While the calculator answer is there, the point should be able to be placed without the calculator… not
exactly, but on the right side of the halfway point.
To find the square root of a number with a TI calculator:
1) Press the “2nd” button
2) Press the “x2” button
3) Type the number you wish to find the square root of.
4) Press “Enter” or “=”
Is the calculator correct when it gives you an answer? Click HERE for the answer on the next slide.
To find the square root of a number with a TI calculator:
1) Press the “2nd” button
2) Press the “x2” button
3) Type the number you wish to find the square root of.
4) Press “Enter” or “=”
Is the calculator correct when it gives you an answer?
If you tried to find the answer to the square root of a non-perfect square number, the calculator is only correct until its last digit. The real answer to the square root of a non-perfect square number is a decimal that goes on forever (non-terminating) without repeating (non-repeating). So the last digit that the calculator shows is rounded… close, but not perfect or exact.
Working with “Uncomfortable” Numbers
Approximation A value close to the
true value but rounded to a whole number or decimal that is more reasonable to work with.
Ex) 3.1415926…
becomes 3.14
Estimate The result of a
calculation using approximated values. The answer will be reasonably close to the true value.
Ex) 5.378 x 6.581
becomes 5 x 7 = 35
Assignment
How to obtain the square root of an imperfect square?
Shortcut:
Let’s say we need to calculate the square root of 95.
Let’s understand the steps:Step 1 : By looking at the number itself,
we can guess, the square root of 95 lies
between 9 and 10.
So, √95=9.__
Step 2 : 95 is 14 more than 92.
Add 14 divided by twice the integer part
of the square root
i.e., 9×2 = 18.
So, the approximate square root of 95 is 9.77 which is very close to 9.747 which
is the actual square-root of 95.
Consider another example, Let’s say we need to calculate the square root of 150.
Step 1 : The square root of 150 lies
between 12 and 13.
So, √150=12.__
Step 2 : 150 is 6 more than 122.
Add 6 divided by twice the
integer part of the square root
i.e., 12×2 = 24.
So, the approximate square root of 150 is 12.25 which is very close to 12.247
which is the actual square-root of 150. Using the same shortcut, can you obtain the square roots ofa)300b)250c)600d)242