1. 9.1 To evaluate square roots Objective Part I Evaluating Square Roots
Square Root of a Number
If , then b is a square root of a.
Example: If 32 = 9, then 3 is a square root of 9.
All positive real numbers have two square roots:
a positive square root (or principal square root) and
a negative square root.
Square roots are written with a radical symbol
The number or expression inside a radical symbol is the radicand.

2. The positive and negative square roots
Meaning
Positive square root
Negative square root
The positive and negative square roots
Symbol
Example
You may use the table on pg 811 to help find square roots

3. You may not have a negative radicand
Example 1
Evaluate the expression. a.
Positive square root b.
Negative square root c.
Square root of zero d.
Two square roots e.
No real square root
You may not have a negative radicand

4.  2.236068… non ending not repeating
Perfect squares: occur when a number is multiplied by itself.
EX: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225
Rational numbers: can be written as a fraction
EX: 4
= 3
An irrational number is a number that cannot be written as a fraction.
They include all non ending non repeating decimals
EX:
 … non ending not repeating
The square roots of numbers that are not perfect squares are irrational numbers and must be written using the radical symbol or approximated.

5. Example 2 Irrational Evaluate the expression. a. b. c. d.
7 is NOT a perfect square

6. Evaluate the expression when a = 1, b = –2, and c = –3 .
Example 3
Evaluate the expression when a = 1, b = –2, and c = –3 .
Substitute values

7. Example 4
Evaluate the expression.
Expression represents two numbers