Download 1-3 - Mr. Raine`s Algebra 2 Class

1-3
1-3 Square
Square Roots
Roots
Warm Up
Lesson Presentation
Lesson Quiz
Holt
Algebra
Holt
Algebra
22
1-3
Square Roots
Warm Up
Round to the nearest tenth.
1. 3.14
3.1
2. 1.97
2.0
Find each square root.
3.
4
4.
25
Write each fraction in simplest form.
5.
6.
Simplify.
7.
Holt Algebra 2
8.
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Square Roots
Objectives
Estimate square roots.
Simplify, add, subtract, multiply,
and divide square roots.
Holt Algebra 2
1-3
Square Roots
Vocabulary
radical symbol
radicand
principal root
rationalize the denominator
like radical terms
Holt Algebra 2
1-3
Square Roots
The side length of a square is the square
root of its area. This relationship is shown
by a radical symbol
. The number or
expression under the radical symbol is
called the radicand. The radical symbol
indicates only the positive square root of a
number, called the principal root. To
indicate both the positive and negative
square roots of a number, use the plus or
minus sign (±).
or –5
Holt Algebra 2
1-3
Square Roots
Numbers such as 25 that have integer
square roots are called perfect squares.
Square roots of integers that are not
perfect squares are irrational numbers. You
can estimate the value of these square
roots by comparing them with perfect
squares. For example,
lies between
and
, so it lies between 2 and 3.
Holt Algebra 2
1-3
Square Roots
Example 1: Estimating Square Roots
Estimate
to the nearest tenth.
<
<
5<
<6
Find the two perfect squares that
27 lies between.
Find the two integers that
lies between
.
Because 27 is closer to 25 than to 36,
Try 5.2: 5.22 = 27.04
5.12 = 26.01
Too high, try 5.1.
Too low
Because 27 is closer to 27.04 than 26.01,
than to 5.1.
Check On a calculator
to the nearest tenth. 
Holt Algebra 2
is close to 5 than to 6.
is closer to 5.2
≈ 5.1961524 ≈ 5.1 rounded
1-3
Square Roots
Check It Out! Example 1
Estimate
<
–7 <
to the nearest tenth.
<
< –8
Find the two perfect squares that
–55 lies between.
Find the two integers that
lies between –
.
Because –55 is closer to –49 than to –64,
is closer to –7
than to –8.
Try 7.2: 7.22 = 51.84
Too low, try 7.4
7.42 = 54.76
Too low but very close
Because 55 is closer to 54.76 than 51.84,
than to 7.2.
is closer to 7.4
Check On a calculator
≈ –7.4161984 ≈ –7.4
rounded to the nearest tenth.
Holt Algebra 2
1-3
Square Roots
Square roots have special properties that help
you simplify, multiply, and divide them.
Holt Algebra 2
1-3
Square Roots
Holt Algebra 2
1-3
Square Roots
Notice that these properties can be used to
combine quantities under the radical
symbol or separate them for the purpose
of simplifying square-root expressions. A
square-root expression is in simplest form
when the radicand has no perfect-square
factors (except 1) and there are no radicals
in the denominator.
Holt Algebra 2
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Square Roots
Example 2: Simplifying Square–Root Expressions
Simplify each expression.
A.
Find a perfect square factor of 32.
Product Property of Square Roots
B.
Quotient Property of Square Roots
Holt Algebra 2
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Square Roots
Example 2: Simplifying Square–Root Expressions
Simplify each expression.
C.
Product Property of Square Roots
D.
Quotient Property of Square Roots
Holt Algebra 2
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Square Roots
Check It Out! Example 2
Simplify each expression.
A.
Find a perfect square factor of 48.
Product Property of Square Roots
B.
Quotient Property of Square Roots
Simplify.
Holt Algebra 2
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Square Roots
Check It Out! Example 2
Simplify each expression.
C.
Product Property of Square Roots
D.
Quotient Property of Square Roots
Holt Algebra 2
1-3
Square Roots
If a fraction has a denominator that is a
square root, you can simplify it by
rationalizing the denominator. To do
this, multiply both the numerator and
denominator by a number that produces a
perfect square under the radical sign in
the denominator.
Holt Algebra 2
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Square Roots
Example 3A: Rationalizing the Denominator
Simplify by rationalizing the denominator.
Multiply by a form of 1.
=2
Holt Algebra 2
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Square Roots
Example 3B: Rationalizing the Denominator
Simplify the expression.
Multiply by a form of 1.
Holt Algebra 2
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Square Roots
Check It Out! Example 3a
Simplify by rationalizing the denominator.
Multiply by a form of 1.
Holt Algebra 2
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Square Roots
Check It Out! Example 3b
Simplify by rationalizing the denominator.
Multiply by a form of 1.
Holt Algebra 2
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Square Roots
Square roots that have the same radicand are
called like radical terms.
To add or subtract square roots, first simplify
each radical term and then combine like
radical terms by adding or subtracting their
coefficients.
Holt Algebra 2
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Square Roots
Example 4A: Adding and Subtracting Square Roots
Add.
Holt Algebra 2
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Square Roots
Example 4B: Adding and Subtracting Square Roots
Subtract.
Simplify radical terms.
Combine like radical terms.
Holt Algebra 2
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Square Roots
Check It Out! Example 4a
Add or subtract.
Combine like radical terms.
Holt Algebra 2
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Square Roots
Check It Out! Example 4b
Add or subtract.
Simplify radical terms.
Combine like radical terms.
Holt Algebra 2
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Square Roots
Lesson Quiz: Part I
1. Estimate
to the nearest tenth.
Simplify each expression.
2.
3.
4.
5.
Holt Algebra 2
6.7
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Square Roots
Lesson Quiz: Part II
Simplify by rationalizing each denominator.
6.
7.
Add or subtract.
8.
9.
Holt Algebra 2