This document discusses square roots and irrational numbers. It defines that the square of an integer is a perfect square, and taking the square root is the opposite of squaring a number. Examples are provided of finding the number that produces a square of 81, which is 9, but -9 also works. The document also defines rational and irrational numbers, noting that square roots of perfect squares are rational, while square roots of non-perfect squares are irrational.

1. Square Roots and
Irrational Numbers

2. 1 2
3
2
1 1= 2
2 4= 2
3 9=
The square of an integer is a
perfect square.
The opposite of squaring a
number is taking the square root.

3. 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

4. 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

5. Simplify each square root
100
16−
Click to the next slide to see solutions.

6. Simplify each square root
 Click to the next slide to see solutions.
100
16−
10

7. Simplify each square root
100
16−
10
-4

8. Squares and Roots
2
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
=
=
=
=
=
=
=
=
=
=
=
=

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

10. 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

11. 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

12. 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

13. TRY THIS:
Estimate to the nearest whole number
27
78−
50
Click to the next slide to see if you are right!

14. TRY THIS:
Estimate to the nearest whole number
27
78−
50
5
-9
7

15.  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.

16. Try This: Identify each number as
rational or irrational
2
81−
0.53
0.627
13.875931...

17. Identify each number as rational or
irrational.
2
81−
0.53
0.627
13.875931...
Irrational
Rational
Rational
Rational
Irrational