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Lesson 7-1:
Radical Expressions
Objectives
Students will:
•Find square roots of numbers
•Find n-th root of numbers
Square Root
The square root of a is c if
c2
=a →
a c
if
c2  a
There are 2 square roots of positive numbers:
c2 = a
(-c)2 = a
and
Example 1 Find the square roots of each:
49
225
Principle Square Root :
,when the positive square root is wanted
Negative Square Root: 
,when the negative square root is wanted
Radicals:
is called a radical sign
Any expression with this sign is a radical expression
The expression under the
is the radicand
Radical Property
The square root of a perfect square is the absolute value of the value
being squared (principle square root)
a2  a
Example 2
(3b) 2 
N-th Roots
3
a c
means c3 = a → c is the “cube root”
Can have 4th roots, 5th roots,….
n
a
is the n-th root of a number
Activity - Find the following:
3
3
4
27
 27
4
5
81
 81
5
243
 243
6
6
Is there a pattern with the answers and the n-value?
729
 729
N-th Root Property
n
an  a
, when n is even (always +)
n
an  a
, when n is odd (can be + or -)
n
 (a)
, does not exist when n is even
n
Determine domain of a root.
(2 x) 2  1
{xlx  }
5x  8
8
{xlx  }
5
x3
x 2  10 x  25
{xlx  3, x  5}
Examples:
3) Give the roots of 169
4) Simplify
 0.04
x 2  18x  81
5) Simplify
6) Simplify
7) Simplify 4
3
64
16t 4
8) Find domain:
3x  2
assignment
7-1/295-296/ 2-64e