square roots & real numbers
TRANSCRIPT
Square Roots & Real Numbers
Holt Algebra I – 1.5
Warm Up Thursday, Sept. 18, 2014
What is the value of x?
1. 4x = 16
2. 5x = 625
Write each number as a power given the base.
3. 10, base 10
4. -64, base -4
Evaluate
5. (-2)4
6. 72
7. -1/24
Tonight’s Homework
O Chapter 1.5, pages 35-36
O #11-15 all, 20-34 all
O Define:
O Real Numbers
O Irrational Numbers
O Natural Numbers
O Whole Numbers
O Integers
O Rational Numbers
Square Roots
O A square root is a number (base), that when
squared, produces a power.
O Squaring and square roots are opposites.
O The radical symbol is used to represent
square roots when placed above a power.
Positive real numbers have two square
roots.
4 4 = 42 = 16 = 4
(–4)(–4) = (–4)2 = 16 – = –4
Positive square
root of 16
Negative square
root of 16
Perfect Squares
O The nonnegative square root is represented
by . The negative square root is
represented by – .
O A perfect square is a number whose positive
square root is a whole number. Some
examples of perfect squares are shown in
the table.
0 1 4 9 16 25 36 49 64 81
0 1 2 3 4 5 6 7 8 9
Practice
1.
2.
3.
4.
Solve
1. .
Think to yourself, “What number squared equals 16?”
2. Think, “What is the opposite of the square root of 9?”
42 = 16
= 4 Positive square root positive 4.
32 = 9
Negative square root negative 3. = –3
Solve
3. .
Think to yourself, “What number squared equals 4?”
4. Think, “What is the opposite of the square root of 25?”
22 = 4
= 2 Positive square root positive 2.
52 = 25
Negative square root negative 5. = –5
Find the square root
Think: What number squared equals 25/81 ?
FYI
O The square roots of many numbers like
are not whole numbers. A calculator can
approximate the value of as
3.872983346... Without a calculator, you
can use square roots of perfect squares to
help estimate the square roots of other
numbers.
Vocabulary!
O Square Root
O Terminating Decimal
O Perfect Square
O Repeating Decimal
O Real Numbers
O Irrational Numbers
O Natural Numbers
O Whole Numbers
O Integers
O Rational Numbers
All numbers that can be represented on a number line are called real numbers and can be classified
according to their characteristics.
Tonight’s Homework
O Chapter 1.5, pages 35-36
O #11-15 all, 20-34 all
O Define:
O Real Numbers
O Irrational Numbers
O Natural Numbers
O Whole Numbers
O Integers
O Rational Numbers