Download Square Roots

9.1
Square Roots
How many squares are on each side of a chessboard?
Goal
Evaluate and
approximate square
roots.
A chessboard is a large square
made up of 64 small squares. In
Exercises 84 and 85, you will use
square roots to investigate whether
game boards of other sizes can
be constructed.
Key Words
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square root
positive square root
negative square root
radicand
perfect square
radical expression
You know how to find the square of a number. For instance, the square of 3 is
32 9. The square of 3 is also 9. In this lesson you will learn about the inverse
operation: finding a square root of a number.
SQUARE ROOT OF A NUMBER
Examples: 32
If b2 a, then b is a square root of a.
9, so 3 is a square root of 9.
(3)2 9, so 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. In the following example, 9 is the radicand. As shown in part (a), the
radical symbol indicates the positive square root of a positive number.
EXAMPLE
1
Read Square Root Symbols
Write the equation in words.
Student Help
READING ALGEBRA
The symbol is read
as “plus or minus” and
is used to write the
positive and negative
square roots of a
positive number.
a. 9
3
b. 9
3
c. 9
3
Solution
Equation
Words
a. 9
3
The positive square root of 9 is 3.
b. 9
3
The negative square root of 9 is 3.
c. 9
3
The positive and negative square roots of 9 are 3 and 3.
Read Square Root Symbols
Write the equation in words.
1. 4
2
2. 2
5 5
3. 1
6 4
9.1
4. 3
6 6
Square Roots
499