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Lesson 3-8
Finding and Estimating Square Roots
Lesson Objectives
1 Find square roots
2 Estimate and use square roots
NAEP 2005 Strand: Number Properties and Operations
Topics: Number Sense; Estimation
Local Standards: ____________________________________
Vocabulary and Key Concepts.
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Square Root
The number a is a square root of b if a 2 Example 42 and (4)2 .
, so 4 and 4 are square roots of
.
The principal square root is
The negative square root of b is
.
The radicand is
Perfect squares are
Examples.
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1 Simplifying Square Root Expressions Simplify each expression.
a. 25
259 b. c. 64
d. 49 e. 0
positive square root
The square roots are
and
.
Negative square root
For real numbers, the square root of
a negative number is
.
There is only one square root of 0.
2 Rational and Irrational Square Roots Tell whether each expression is rational
or irrational.
a. 144 b.
15
0.44721359. . .
c. 6.25 d.
19 0.3
e. 7 Daily Notetaking Guide
Algebra 1 Lesson 3-8
63
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3 Estimating Square Roots Between what two consecutive integers is Î 28.34 ?
28.34 28.34 is between the two consecutive
perfect squares
28.34 Î 28.34 is between
and
.
The square roots of 25 and 36 are
and
and
, respectively.
.
4 Applying Square Roots Suppose a rectangular field has a length y three
times its width x. The formula d Î x2 1 y2 gives the length of the diagonal
d x2 (3x)2
d d d 2
Substitute 3x for
)2
(3 ?
Substitute
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of a rectangle. Find the distance of the diagonal across the field if x = 8 ft.
.
for x.
Simplify.
d
Use a calculator. Round to the nearest tenth.
The diagonal is about
ft long.
1. Simplify each expression.
a. Î 49
b. Î 36
c. Î 121
d. Î 25
1
2. Tell whether each expression is rational or irrational.
a. Î 8
b. Î 225
c. Î 75
d. Î 14
3. Between what two consecutive integers is Î 105?
4. Using the formula from Example 4, suppose x 10 ft. How long is the diagonal
across the field? Round to the nearest tenth of a foot.
64
Algebra 1 Lesson 3-8
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