1. Evaluating Square Roots
Chapter 9 Section 1

2. Learning Objective Evaluate Square Roots of real numbers
Recognize that not all square roots represents real numbers
Determine whether the square root of a real number is rational or irrational
Write square roots as exponential expressions

3. Key Vocabulary square root root principal square root imaginary
radical sign
radicand
radical expression
index
root
imaginary
perfect square
perfect square factor
rational number
irrational number

4. Evaluate Square Roots of Real Numbers
positive or principal square root uses the to indicate a positive square root if
“The square root of a”
Negative square roots are indicated by

5. Evaluate Square Roots of Real Numbers
radical sign is
radicand is the number under the radical sign
radical expression is the entire expression
Index tells the root of the expression and the squared root index are not written
All squares of a nonzero real number must be positive

6. Evaluate Square Roots of Real Numbers
square root is the reverse process of squaring a number
Example : because 72 = (7)(7) = 49
The is 0, written

7. Evaluate Square Roots of Real Numbers
Examples:

8. Evaluate Square Roots of Real Numbers
Examples:

9. Negative Square Roots Negative square roots are not real numbers
How do we know that the square of any nonzero real number must be a positive number? Example:

10. Perfect Squares
The numbers 1, 4, 9, 16, 25, 36, 49, … are perfect squares because each number is a square of a natural number.
See page 536 for a list of the first 20 perfect squares.
Natural numbers
Square Natural number
Perfect squares

11. Rational Numbers
A rational number can be written as a and b are integers and b ≠ 0
Rational numbers written as a decimal are either terminating or repeating. ½ = or ⅓ = .333…
Round you answers two decimal place and use the approximately equal sign ≈

12. Rational Numbers
The square root of every perfect square is also a rational number.

13. Irrational Numbers
A irrational number is any number that is not rational and are non-terminating and non-repeating decimals.
The square root of non perfect square are irrational number

14. Writing a Square Root in Exponential Form
Reviewing the rules for exponents in chapter 4 section 1 and 2 may be helpful.

15. Writing a Square Root in Exponential Form

16. Review of Rules for Exponents
Product Rule:
Quotient Rule:
Zero Exponent Rule:

17. Review of Rules for Exponents
Power Rule:
Expanded Power Rule:
Negative Exponent Rule:

18. Remember
The square root is the opposite or reverse process of squaring.
“Square of a number”
“Multiply the number by itself”
Every real number greater than 0 has two squares one positive and one negative
Square roots of negative numbers are not real numbers. They are imaginary numbers

19. Remember The results of a square root is always nonnegative.
The result is only rational if the radicand is a perfect square
The radical form is the exact value.
Calculators only give approximate values for irrational numbers. We use the ≈ sign for these values.

20. Remember
You should try to memorize as many perfect squares as possible to help with simplifying in the next section.
Review of factoring may also be helpful for simplifying in the next section.
Extra practice may be helpful to remember the difference between and

21. HOMEWORK 9.1
Page # 13, 21, 23, 31, 33, 37, 41, 65, 71, 74