Take Note Key Concept: Multiplying Real Numbers

Words	The product of two real numbers with different signs is negative.	Model 2 ( − 3 ) = − 6 2 open negative 3 close equals negative 6
Examples	2 ( − 3 ) = − 6 − 2 · 3 = − 6 2 open negative 3 close equals negative 6 minus 2 middle dot 3 equals negative 6
Words	The product of two real numbers with the same sign is positive.	Model 2 · 3 = 6 2 middle dot 3 equals 6
Examples	2 · 3 = 6 − 2 ( − 3 ) = 6 2 middle dot 3 equals 6 minus 2 open negative 3 close equals 6

Problem 1 Multiplying Real Numbers

What is each product?

✓ Got It?

1. What is each product?
   1. 6 ( − 15 ) 6 open negative 15 close
   2. 12(0.2)
   3. − 7 10 ( 3 5 ) negative , 7 tenths . open , 3 fifths , close
   4. ( − 4 ) 2 open negative 4 close squared

Problem 2 Simplifying Square Root Expressions

What is the simplified form of each expression?

1. − 25 = − 5 ( − 5 ) 2 = 25 ,  so  − 25 = − 5 negative square root of 25 equals negative 5 . open , negative 5 , close squared . equals 25 comma , so , minus square root of 25 equals negative 5
2. ± 4 49 = ± 2 7 ( 2 7 ) 2 = 4 49  and  ( − 2 7 ) 2 = 4 49 ,  so  ± 4 49 = ± 2 7 plus minus , square root of 4 forty ninths end root , equals plus minus , 2 sevenths . open , 2 sevenths , close squared . equals , 4 forty ninths . and . open , negative , 2 sevenths , close squared . equals , 4 forty ninths , comma , so , plus minus , square root of 4 forty ninths end root , equals plus minus , 2 sevenths

✓ Got It?

2. What is the simplified form of each expression?
   1. 64 square root of 64
   2. ± 16 plus minus square root of 16
   3. − 121 negative , square root of 121
   4. ± 1 36 plus minus , square root of 1 thirty sixth end root