Transcript Operations with Radicals

Operations with
Radicals
Lesson 13.3
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
Like Radicals…





Two radical expressions are like
radicals if they have the same
radicand.
For instance, √2 and 3√2 are like
radicals.
To add or subtract like radicals, add
or subtract their coefficients.
√2 + 3√2 = (1 + 3)√2 = 4√2
√2 - 3√2 = (1 – 3)√2 = -2√2
Practice…
1.
2√3 + √2 - 4√3
1.
2.
-2√3 + √2
Add like radicals.
3√2 - √8
1.
2.
3.
3√2 - √4 ∙ √2
3√2 - 2√2
√2
Product Property
Subtract like radicals.
Multiplying Radicals

3√2(√2 + 4√6)
 = (3√2)(√2) + (3√2)(4√6)
Distributive Property
 = 3(√2 ∙ √2) + (3∙4)(√2∙ √6)
Regroup
 = 3√4 + 12√12
Product Property
 = 3√4 + 12√4∙3
Perfect square factor
 = 3(2) + 12(2)√3
Simplify
 = 6 + 24√3
Simplest form
Practice: simplify the radical
expressions.
1.
4√3 - 5√3
-√3
2.
-6√12 + √75
-6√4∙3 + √25∙3
-12√3 + 5√3
-7√3
Multiply and Simplify
1.
2√3(√2 + 5√6)
2√6 + 10√18
2√6 + 10√9∙2
2√6 + 30√2
2.
3√8(√3 – 5)
3√24 - 15√8
3√(4•6) - 15√(4•2)
(3•2)√6 - 15•2√2
6√6 - 30√2