1. Non-Perfect Squares 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)

2. Perfect Squares (a review)1) 2) 3) 4) 5) 6) 7) 8) 9)
10)
11)
12)
13)
14)
15)
16)
17)
18)
19)
20)
21)

3. Perfect Squares (a review)
Answers 1) 5 2) 13 3) 1 4) 12 5) 7 6) 30 7) 2 8) 15 9) 4
10) 10
11) 6
12) 14
13)
14) 3
15) 8 70
16) 11
17) 40
18) 20
19) 9
20)
120
21)
100

4. Non-Perfect Squares Here is the list of perfect squares from 1 to 256.
Not every number is a perfect square.
If they aren’t, we call them non-perfect squares.
To find the square root of a number that is not a perfect square, we use estimation with perfect squares.

5. Non-Perfect Squares
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.
Using the above information (which we should have memorized), what two numbers would the answer to be between?
Since 10 is between 9 and 16, the answer to is between the answer to and the answer to

6. Non-Perfect Squares
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. 3
3.5 4 …
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.

7. 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.

8. 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.

9. 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) …
becomes
Estimate
The result of a calculation using approximated values. The answer will be reasonably close to the true value.
Ex) x 6.581
becomes 5 x 7 = 35

10. Assignment

11. How to obtain the square root of an imperfect square?
Shortcut: Let’s say we need to calculate the square root of 95.

12. 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.

13. So, the approximate square root of 95 is 9.77 which is very close to which is the actual square-root of 95.

14. Consider another example, Let’s say we need to calculate the square root of 150.

15. Step 1 : The square root of 150 lies between 12 and 13. So, √150=12
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.

16. Using the same shortcut, can you obtain the square roots of 300 250
So, the approximate square root of 150 is which is very close to which is the actual square-root of 150.
Using the same shortcut, can you obtain the square roots of
300
250
600
242