1. Objectives Evaluate expressions containing square roots.
Classify numbers within the real number system.

2. Finding the Square Root of a number is the opposite
A Square Root is when you have the product of a number multiplied by itself. The answer to a square root is the number that multiples by itself.
Finding the Square Root of a number is the opposite
of Squaring a number
The radical (root) symbol , is used to represent square roots. Square roots have two answers (one positive and one negative).
Positive square
root of 16
4  4 = 42 = 16
= 4 –
Negative square
root of 16
(–4)(–4) = (–4)2 = 16
= –4

3. A perfect square is a number whose positive square root answer is a whole number. Some examples of perfect squares are shown in the table. 1 4 9 16 25 36 49 64 81
100 02 12 22 32 42 52 62 72 82 92
102

4. The expression does not represent
a real number because there is no real number that can be multiplied by itself to make a negative number.
You cannot square root a negative number!!
Reading Math

5. Example 1: Finding Square Roots of
Perfect Squares
Find each square root. A.
Think: What number squared equals 16?
42 = 16
Positive square root positive 4.
= 4 B.
Think: What is the opposite of the
square root of 9?
32 = 9
= –3
Negative square root negative 3.

6. Check It Out! Example 1
Find the square root.
1a.
22 = 4
Think: What number squared
equals 4?
= 2
Positive square root positive 2.
1b.
52 = 25
Think: What is the opposite of the square root of 25?
Negative square root negative 5.

7. Check It Out! Example 1
Find the square root.
1b.
The 36 is negative, so you can’t square root it

8. Example 1C: Finding Square Roots of
Perfect Squares
Find the square root.
Think: What number squared equals ? 25 81
Positive square root positive . 5 9

9. The square roots of many numbers like , are not whole numbers
The square roots of many numbers like , are not whole numbers. A calculator can approximate the value of as Without a calculator, you can use square roots of perfect squares to help estimate the square roots of other numbers.

10. Think about the perfect squares above and below 13.
Example 2
Find
Think about the perfect squares above and
below 13.
These are and
Now find the square roots of those to find
out between which two numbers is.
You can then use guess and check to find
out which decimal between 3 and 4 it is.

11. All numbers that can be represented on a number line are called real numbers and can be classified according to their characteristics.

12. Natural numbers are the counting numbers: 1, 2, 3, …
Whole numbers are the natural numbers and zero:
0, 1, 2, 3, …
Integers are whole numbers and their opposites: –3, –2, –1, 0, 1, 2, 3, …
Rational numbers can be expressed in the form ,
where a and b are both integers and b ≠ 0: , , . a b 1 2 7 9 10

13. Terminating decimals are rational numbers in
decimal form that have a finite number of digits:
1.5, 2.75, 4.0
Repeating decimals are rational numbers in
decimal form that have a block of one or more
digits that repeat continuously: 1.3, 0.6, 2.14
Irrational numbers cannot be expressed in the form . They include square roots of whole numbers that are not perfect squares and nonterminating decimals that do not repeat: ,
,  a b