Transcript Holt McDougal Algebra 2 1-3

1-3
1-3 Square
Square Roots
Roots
Warm Up
Lesson Presentation
Lesson Quiz
Holt McDougal Algebra 2
1-3
Square Roots
Opener-SAME SHEET-3/21
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 McDougal Algebra 2
8.
1-3
Square Roots
• Graph Paper Squares
On graph paper, make squares that have
sides lengths, 1-15.
Calculate the area, then find the square root
Holt McDougal Algebra 2
1-3
Square Roots
Website
Holt McDougal Algebra 2
1-3
Square Roots
Objectives
Estimate square roots.
Simplify, add, subtract, multiply,
and divide square roots.
Holt McDougal Algebra 2
1-3
Square Roots
Vocabulary
radical symbol
radicand
principal root
rationalize the denominator
like radical terms
Holt McDougal 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 McDougal 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 McDougal Algebra 2
1-3
Square Roots
Example 1: Estimating Square Roots
Estimate
to the nearest tenth.
Check On a calculator
to the nearest tenth. 
Holt McDougal Algebra 2
≈ 5.1961524 ≈ 5.1 rounded
1-3
Square Roots
Check It Out! Example 1
Estimate
to the nearest tenth.
Check On a calculator
≈ –7.4161984 ≈ –7.4
rounded to the nearest tenth.
Holt McDougal Algebra 2
1-3
Square Roots
Number Line
• Place your sticky note in between the two
whole numbers.
Holt McDougal Algebra 2
1-3
Square Roots
Reteach(4-6)
Holt McDougal Algebra 2
1-3
Square Roots
Holt McDougal Algebra 2
1-3
Square Roots
Square roots have special properties that help
you simplify, multiply, and divide them.
Holt McDougal Algebra 2
1-3
Square Roots
Holt McDougal 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 McDougal Algebra 2
1-3
Square Roots
Example 2: Simplifying Square–Root Expressions
Simplify each expression.
A.
B.
C.
Holt McDougal Algebra 2
D.
1-3
Square Roots
Check It Out! Example 2
Simplify each expression.
A.
C.
Holt McDougal Algebra 2
B.
D.
1-3
Square Roots
Opener-SAME SHEET-3/22
1. Estimate
to the nearest tenth.
Simplify each expression.
2.
3.
4.
5.
Holt McDougal Algebra 2
6.7
1-3
Square Roots
Holt McDougal Algebra 2
1-3
Square Roots
Holt McDougal Algebra 2
1-3
Square Roots
I have, Who has?
Holt McDougal 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 McDougal Algebra 2
1-3
Square Roots
Example 3A: Rationalizing the Denominator
Simplify by rationalizing the denominator.
Holt McDougal Algebra 2
1-3
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 McDougal Algebra 2
1-3
Square Roots
Example 4A: Adding and Subtracting Square Roots
Add.
Holt McDougal Algebra 2
1-3
Square Roots
Opener-SAME SHEET-3/25
Simplify by rationalizing each denominator.
6.
7.
Add or subtract.
8.
9.
Holt McDougal Algebra 2
1-3
Square Roots
Wkst
Holt McDougal Algebra 2
1-3
Square Roots
Holt McDougal Algebra 2
1-3
Square Roots
Holt McDougal Algebra 2
1-3
Square Roots
Quiz
Holt McDougal Algebra 2