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Roots and Irrational Numbers
Lesson Quiz: Part I
Give two ways to write each algebraic
expression in words.
1. j – 3
Possible answers:
The difference of j and 3; 3 less than j.
2. 4p
Possible answers:
4 times p; The product of 4 and p.
3. Mark is 5 years older than Juan, who is y years
old. Write an expression for Mark’s age.
y+5
Roots and Irrational Numbers
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Lesson Quiz: Part II
Evaluate each expression for the replacement
set {5, 8, 12}.
d
4. 2
5
; 4; 6
2
Shemika practices basketball for 2 hours each
day.
5. Write an expression for the number of hours she
practices in d days.
2d
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Roots and Irrational Numbers
California
Standards
2.0 Students understand and use such
operations as taking the opposite, finding the
reciprocal, taking a root, and raising to a
fractional power. They understand and use the
rules of exponents.
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Roots and Irrational Numbers
Vocabulary
perfect square
square root
cube root
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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
02
12
22 32
16 25 36 49 64 81 100
42 52
62
72
82
92 102
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Roots and Irrational Numbers
A number that is multiplied by itself to form a
product is a square root of that product. The
radical symbol
is used to represent square
roots.
STOP: You cannot take the square root of a
negative number
4  4 = 42 = 16
(–4)(–4) = (–4)2 = 16
–
=4
Positive square
root of 16
= –4
Negative square
root of 16
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Roots and Irrational Numbers
A number that is raised to the third power to form
a product is a cube root of that product. The
symbol
indicates a cube root. Since 23 = 8,
= 2. Similarly, the symbol
indicates a fourth
root: 2 = 16, so
= 2.
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Roots and Irrational Numbers
Additional Example 1: Finding Roots
Find each root.
Think: What number squared equals 81?
Think: What number squared equals 25?
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Additional Example 2: Finding Roots of Fractions
Find the root.
A.
Think: What number squared
equals
Roots and Irrational Numbers
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Additional Example 2: Finding Roots of Fractions
Find the root.
B.
Think: What number cubed equals
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Additional Example 2: Finding Roots of Fractions
Find the root.
C.
Think: What number squared
equals
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Roots and Irrational Numbers
Additional Example 3: Art Application
As part of her art project, Shonda will need to
make a paper square covered in glitter. Her
tube of glitter covers 13 in². Estimate to the
nearest tenth the side length of a square with
an area of 13 in².
Since the area of the square is 13 in², then each
side of the square is
in. 13 is not a perfect
square, so find two consecutive perfect squares
that
is between: 9 and 16.
is between
and
, or 3 and 4. Refine the estimate.
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Roots and Irrational Numbers
Check It Out! Example 3
What if…? Nancy decides to buy more wildflower
seeds and now has enough to cover 26 ft2.
Estimate to the nearest tenth the side length of a
square garden with an area of 26 ft2.
Since the area of the square is 26 ft², then each
side of the square is
ft. 26 is not a perfect
square, so find two consecutive perfect squares
that
is between: 25 and 36.
is between
and
, or 5 and 6. Refine the estimate.