Download Simplifying Radicals

Simplifying
Radicals
Lesson 13.2
Learning Goal 1 (HS.N-RN.B3 and HS.A-SSE.A.1):
The student will be able to use properties of rational and
irrational numbers to write, simplify, and interpret expressions
based on contextual situations.
4
3
In addition to
level 3.0 and
above and
beyond what
was taught in
class, the
student may:
·
Make
connection with
other concepts
in math
·
Make
connection with
other content
areas.
The student will be
able to use properties
of rational and
irrational numbers
to write, simplify, and
interpret expressions
on contextual
situations.
- justify the sums and
products of rational
and irrational numbers
-interpret expressions
within the context of a
problem
2
1
0
The student will
With help
Even with
be able to use
from the
help, the
properties of
teacher, the student has
rational and
student has no success
irrational
partial
with real
numbers to write success with
number
and
real number expressions.
simplify expressi expressions.
ons based on
contextual
situations.
-identify parts of
an
expression as
related to the
context and to
each part
An expression with radicals is in
simplest form if the following are true:
1. No radicands (expressions under radical
signs) have perfect square factors other
than 1.
82 2
2. No radicands contain fractions.
7
7

9
3
3. No radicals appear in the denominator of
a fraction.
1
1
4

2
Product Property
• The square root of a product equals
the product of the square root of the
factors.
ab  a  b
• For example:
50  25  2
5 2
Quotient Property
• The square root of a quotient equals the
quotient of the square root of the
numerator and denominator.
a
a

b
b
• For example:
3

4
3
4
3

2
If the radical in the denominator is not
the square root of a perfect square,
then a different strategy is required.
Simplify
1 .
To simplify this expression,
multiply the numerator and
denominator by √2.
2
1
1
2


2
2
2
1 2

2 2
2

4
2
2
Practice…
1.
75
 25  3  5 3
2.
180
 36  5  6 5
3.
49
121
49

121
4.
3
12
1
5. .
8
=
7

11
3 ∙ √12 = 3 ∙ 2√3
√12 √12
12
= √1 ∙ √8
√8 √8
= √8
8
= √3
2
= 2√2 = √2
2∙4
4
Find the area of a rectangle…
• Find the area of a rectangle whose width is
√2 inches and whose length is √30 inches.
Give the result in exact form (simplified) and
in decimal form.
Area = Length ∙ Width
√30 in.
√2 in.
= √30 ∙ √2
= √60
= √4 ∙ √15
= 2√15
about 7.746 square inches.