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Multiplying Cube Roots

Example 1

Find:

Solution
Distribute
In the first term, multiply the radicands.
Simplify  
The radicand, 24, has a perfect cube factor, 8.

So, write 24 as the product 8 · 3.
Rewrite as the product
Simplify .
Write 7 to the left of

So,

 

Note:

If you have difficulty “seeing” that 24 has a perfect cube factor, find the prime factorization of 24.

24 = 2 · 2 · 2 · 3

= 23 · 3
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