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Positive real numbers have two square roots.
Zero has only one square root: zero. Negative numbers do not have real square
roots because the square of every real number is either positive or zero.
NUMBER OF SQUARE ROOTS
Student Help
EXAMPLE
READING ALGEBRA
Since negative
numbers do not have
real square roots, we
64
is
say that undefined.
2
Find Square Roots of Numbers
Evaluate the expression.
a. 6
4
b. 6
4
c. 6
4
82 8
b. 6
4 82 8
c. 6
4 82 8
a. 6
4 Solution
d. 0
0
d. 0
Positive square root
Negative square root
Two square roots
Square root of zero is zero.
Find Square Roots of Numbers
Evaluate the expression.
5. 1
00
6. 2
5
7. 3
6
8. 1
6
The square of an integer is called a perfect square. Of course a square root of a
perfect square is an integer. On the other hand, if n is a positive integer that is not
a perfect square, then it can be shown that n is an irrational number. An
irrational number is a number that is not the quotient of integers. In Lesson 12.9
you will use an indirect proof to prove that 2 is an irrational number.
4 2
4 is a perfect square.
4 is an integer.
2 ≈ 1.414
2 is not a perfect square.
2 is neither an integer nor a
rational number.
EXAMPLE
Student Help
STUDY TIP
You can use a
calculator or the Table
of Square Roots on
p. 801 to approximate
an irrational square
root.
3
Evaluate Square Roots of Numbers
Evaluate the expression. Give the exact value if possible. Otherwise,
approximate to the nearest hundredth.
a. 4
9
Solution
b. 3
a. 4
9 72 7
49 is a perfect square.
b. 3
≈ 1.73
Round to nearest hundredth.
Evaluate Square Roots of Numbers
Evaluate the expression. Give the exact value if possible. Otherwise,
approximate to the nearest hundredth.
9. 1
00
500
Chapter 9
10. 5
Quadratic Equations and Functions
11. 2
3
12. 8
1