SOLUTION: Please tell me the solution of 2.cube root 4 * 3.cube root 16. Answer is coming 24 but i want to know the solution how it came.

Algebra ->  Square-cubic-other-roots -> SOLUTION: Please tell me the solution of 2.cube root 4 * 3.cube root 16. Answer is coming 24 but i want to know the solution how it came.       Log On


   

Question 1085563: Please tell me the solution of 2.cube root 4 * 3.cube root 16. Answer is coming 24 but i want to know the solution how it came.

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
%282%2Aroot%283%2C4%29%29%2A%283%2Aroot%283%2C16%29%29

Take away the parentheses

2%2Aroot%283%2C4%29%2A3%2Aroot%283%2C16%29

Rearrange the factors

2%2A3%2Aroot%283%2C4%29%2Aroot%283%2C16%29

Since  2•3 = 6, we have:

6%2Aroot%283%2C4%29%2Aroot%283%2C16%29

Those roots have the same index, so
we can multiply the numbers under
them an just have one cube root:

6%2Aroot%283%2C4%2A16%29

And since 4•16 = 64,

6%2Aroot%283%2C64%29

Maybe you already know that the cube root of 64 is 4, and
that you'd have 6•4 which is 24. But if you don't you can 
do this instead:

Break 64 down like this:
64 = 4•4•4 = 43, so we have:

6%2Aroot%283%2C4%5E3%29

When the index of the root and the exponent
of the radicand are the same, the cube root
cancels out the cube:

6%2Aroot%28cross%283%29%2C4%5Ecross%283%29%29

and all that's left is the number under the
radical:

6%2A4%29

And that's just

24

Edwin