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