Square Roots and Irrational Numbers

1 23

21 1 22 4 23 9

The square of an integer is a perfect square.

The opposite of squaring a number is taking the square root.

Example

For example

asks what number multiplied by itself is equal to 81? That number is 9.

Is there another solution to that problem?

81

Example

For example

asks what number multiplied by itself is equal to 81? That number is 9.

Is there another solution to that problem?

Yes, -9 is also a solution.

81

Simplify each square root

100

16

Click to the next slide to see solutions.

Simplify each square root

Click to the next slide to see solutions.

100

16

10

Simplify each square root

100

16

10

-4

Squares and Roots2

2

2

2

2

2

2

2

2

2

2

2

1 1

2 4

3 9

4 16

5 25

6 36

7 49

8 64

9 81

10 100

11 121

12 144

1 1

4 2

9 3

16 4

25 5

36 6

49 7

64 8

81 9

100 10

121 11

144 12

Note!!!

Notice that squares and square roots are inverses (opposites) of each other.

Estimating Square Roots

Once you memorized squares and their roots, we can estimate square roots that are not perfect squares

For example, what about 8

Estimating Square Roots

We find the two perfect squares that are before and after the square root of 8. . .

and

Look at them on a number line:

4

9

5

4

96 7 832

2 3

Estimating square roots

We can see that is between 2 and 3 but

is closer to 3. We would say that is approximately 3.

4 5 96 7 832

2 3

8

8

TRY THIS:Estimate to the nearest whole number

27

78

50

Click to the next slide to see if you are right!

TRY THIS:Estimate to the nearest whole number

27

78

50

5

-9

7

Rational number- can be written as a fraction

Irrational number- cannot be written as a fraction because:

• it is a non-terminating decimal• it is a decimal that does NOT repeat

* The square roots of ALL perfect squares are rational.

* The square roots of numbers that are NOT perfect squares are irrational.

Try This: Identify each number as rational or irrational

2

81

0.53

0.627

13.875931...

Identify each number as rational or irrational.

2

81

0.53

0.627

13.875931...

Irrational

Rational

Rational

Rational

Irrational