Algebra 1 Common Core Student Edition, Grade 8-9

What is your first step

in finding a product o f

real numbers?

Id e n tify th e signs o f the

factors. Then determ ine

the sign o f the product.

How can you find
a n e g ative square
root?
Look fo r a n e g a tive
n u m ber th a t you can
multiply by itself to get a
p ro d u ct th a t is equal to
the radicand.

Key Concep t M ultiplying Real Num bers

Words T h e p r o d u c t o f t w o r e a l n u m b e r s w i t h Model 2(—3) = -6

different s i g n s i s negative. ^ 3

Examples 2(-3) = -6 -2 • 3 = -6 , j * , | j* , ~ \ , ,

-6 -5 -4 -3 - 2 - 1 0 1

Words T h e p r o d u c t o f t w o r e a l n u m b e r s w i t h th e Model 2*3 = 6

same s ig n is positive. 3 3

I--------------------H---—---------H

Examples 2 *3 = 6 -2(-3) = 6 i------ 1 ------ 1 ------ 1 ------ 1 ------ 1 ------ 1 ------t—»-

-1 0 1 2 3 4 5 6

V ,------------------------------^—m___, , ( wmmmmmm y

Multiplying Real Numbers

What is each product?

Q l 2 ( - 8 ) = - 9 6 The p ro d u ct o f tw o num bers w ith d iffe re n t signs is negative.

0 24(0.5) = 1 2 The p ro d u ct o f tw o num bers w ith th e same sign is positive.

0 | The p ro d u c t o f tw o num bers w ith d iffe re n t signs is negative.

0 ( ~ 3 ) 2 = (—3)(—3) = 9 The p ro d u ct o f tw o num bers w ith the same sign is positive.

Got It? 1 ■ W h a t is e a c h p r o d u c t?

a. 6(—15) b. 12(0.2) c. -^ (§ ) d. (-4 )2

Notice that (-3)2 = 9 i n p a r t ( d ) o f P r o b le m 1. Recall from Lesson 1-3 t h a t a is a s q u a re

ro o t o f b i f a2 = b. So, —3 is a s q u a r e r o o t o f 9. A n e g a tiv e s q u a r e r o o t is r e p r e s e n te d b y

— V ". E v e r y p o s it iv e r e a l n u m b e r h a s a p o s it iv e a n d a n e g a tiv e s q u a r e r o o t. T h e s y m b o l

± i n f r o n t o f th e r a d ic a l i n d ic a t e s b o t h s q u a r e r o o ts.

Simplifying Square Root Expressions

What is the simplified form of each expression?

0 — V25 = —5 (—5)2 = 25, so — V25 = -5.

0 ± \/5 - ± Ml)2 - ® bfl2 - i »± v l - ± f

G ot It? 2. What is the simplified form of each expression?

a. V 6 4 b. ±vT6 c. -V m d .± \/^

C

PowerAlgebra.com | Le sso n 1 b 6 Multiplying and Dividing Real Numbers 39