You may need to simplify radical expressions first to determine if they can be added or
subtracted by combining like radicals.1 i l l t l f€.
How do you know if
radical expressions
can be combined?
Simplify all radicals.
Although V 3 and V T I
are unlike radicals, they
can be com bined after
VT 2 is sim p lifie d.Pr o b l em 2 Si m p l i f y i n g t o Co m b i n e Li k e Ra d i c a l s
What is the simplified form of 5 V 3 - V l 2?
5 V3 - V l 2 = 5 V3 - V4 • 3 4 is a p e rfe c t-s q u a re fa c to r o f 12.
= 5 V 3 - Vi • V 3 M u ltip lic a tio n P ro p e rty o f S quare Roots
= 5V3 —2V3 Simplify V4.
= (5 - 2) V 3 Use the Distributive Property to combine like radicals.
= 3V 3 Simplify.Go t I t? 2. What is the simplified form of each expression in parts (a) and (b)?
a. 4 V7 + 2 V2I3 b. 5V32-4A/I8
c. Reaso n i n g Can you combine two unlike radicals when the radicands
have no common factors other than 1? Explain.When simplifying a product like VTo( V 6 + 3), you can use the Distributive Property
to multiply Vl O times V6 and Vl O times 3. If both factors in the product have two
terms, as in (V 6 — 2 V3)( V6 + V3), you can use FOIL to multiply just as you do
when multiplying binomials.Think
Have you seen a
problem like this
before?
Yes. Parts (A) and (B) are
similar to simplifying
products like 3(x + 2 )
and (2x + 1)(x - 5).
Pr o b l em 3 Multiplying Radical Expressions
What is the simplified form of each expression?
Q Vl0(V6 + 3)
vTo(Ve + 3) = (V io • V6) + (vTo • 3)
= V60 + 3 V I0
= V4 • V l 5 + 3 V T o
= 2 V l 5 + 3 V l O
Q(V6 - 2V3)(V6 + V3)
(V6 - 2 V3)( V6 + V3) = V36 + V l8 - 2 V l8 - 2 V9= 6 - V18 - 2(3)= 6 - V9 • V2-6= -3V 2Distributive Property
Multiplication Property of Square Roots
4 is a p e rfe c t-s q u a re fa c to r o f 60.
Simplify V 4.Use FOIL.
Combine like radicals
and simplify.
9 is a p e rfe c t-s q u a re
fa cto r o f 18.
Simplify.& Got It? 3. What is the simplified form of each expression?
a. V2( V6 + 5) b. (VII - 2)2 c. (V6 - 2 V3)(4 V3 3V6)Lesson 10-3 Operations With Radical Expressions^627