Lesson Vocabulary

• simplest form of a radical
• rationalize the denominator

Take Note Property: Combining Radical Expressions: Products

If a n the th , root of eh ,  and b n the th , root of b ,  are real numbers, then a n ⋅ b n = a b n . the th , root of eh , , dot , the th , root of b , , equals , the th , root of eh b end root , , .

Problem 1 Multiplying Radical Expressions

Can you simplify the product of the radical expressions? Explain.

1. 6 3 ⋅ 2 cube root of 6 , , dot square root of 2

   Plan

   What allows you to use the property for multiplying radicals?

   The radicals must be real numbers. The indexes must be the same.

   No. The indexes are different. The property above does not apply.

2. − 4 3 ⋅ 2 3 cube root of negative 4 end root , , dot , cube root of 2 ,

   yes. − 4 3 ⋅ 2 3 = − 4 ( 2 ) 3 = − 8 3 = − 2 . cube root of negative 4 end root , , dot , cube root of 2 , , equals . cube root of negative 4 , open 2 close end root , . equals , cube root of negative 8 end root , , equals negative 2 .