Objectives To simplify sums and differences of radical expressions
To simplify products and quotients of radical expressionsOperations With
Radical Expressions
@ Common Core State Standards
Prepares for A-REI.A.2 Solve sim ple rational and
radical equations in one variable, and give examples
showing ho w extraneous solutions may arise.
MP 1, MP 2, MP3, MP 4, MP 7Lesson
Vocabulary
lik e ra d icals- un like radicals
- c o n ju g a te s
it-For example, you can use the Distributive Property to simplify sums or
differences of radical expressions by combining like radicals. Like radicals,
such as 3 V5 and 7 V5, have the same radicand. Unlike radicals, such as
4 V3 and —2 V2, have different radicands.Have you seen a
problem like this
before?
Yes. C o m b in in g lik e
radicals is s im ila r to
co m b in in g like term s. For
example, sim plifying the
expression in p a rt (A)
is s im ila r to s im p lifyin g
6x + 9x.Pr o b l em 1 Co m b i n i n g Li k e Ra d i c a l s
What is the simplified form of each expression?06VIT + 9 VFT
6 VII + 9 vTT = (6 + 9) vTT Use the D istributive Property to com bine like radicals.
= 15VTT Simplify.
Q V 3 - 5 V 3
V3 — 5 V3 = 1V3 — 5 V3 Write V3 as 1V3.
= (1 - 5) V3 Use th e D istributive Property to com bine like radicals.
= -4V3 Simplify.Get t i n g Read y! 4* X C -A v o lu n te e r is b u ild in g a n e w ra m p
fo r a toy car derby. The ramp
takes th e car down th e two steps
shown in t h e d ia g r a m. H o w long
should th e volunteer m ake th e ram p?
Justify your reasoning.Notice that
th e ramp is th e
hypotenuse of two
right triangles. This
should help you g e t
started.MAt HEMAt i CAL Esse n t i a l U n d e r st a n d i n g You can use properties of real numbers to
PRACTICES perform operations with radical expressions.sj Go t I t? 1. What is the simplified form of each expression?
a. 7V2-8V2 b. 5V5 + 2V5626 Chapter 10 Radical Expressions and Equations