Urgent ! which of the following best defines ? square root of 16 cube root of 4 square root of 4 cube root of 16 square root of 16 cube root of 4 square root of 4 cube root of 16

The answer is:  "  16 * ∛12 " ; or, write as:  " 35.631 " .

Explanation:


" Square root of 16 Cube root of 4 Square root of 4 Cube root of 16"  =

√16 * ∛6 *√4 *∛16 = 

√16 * √4 * ∛6 * ∛16 = 

4 * 2 * ∛6 * ∛16 =

8 * (∛6 * ∛16) = 

8 * (∛(6 * 16) =

8 * (∛96) = ?

What are the factors of "96" ?  And do any of them have "perfect cube"? (since "96" does not) ??

96:  1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96.
Not:  "8" is a perfect cube:  ∛8 = 2 ;

and:  "8 * 12 = 96" ;

  So;  ∛(96) = ∛8 * ∛(12) = 2* ∛(12) .

and:  

 8 * (∛96) = 8 * 2 * ∛(12) ;

                 = 16 * ∛12 ;  or, use a calculator to multiply to find the value:

                 = 36.6308557617066198 ;  round to 35.631   .