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.Com
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)   (Show Source): You can put this solution on YOUR website!


Take away the parentheses



Rearrange the factors



Since  2•3 = 6, we have:



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



And since 4•16 = 64,



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:



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



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



And that's just



Edwin


RELATED QUESTIONS

how to solve= 1/cube root 4+ cube root 2 +1 i know the ans is cube root 2 -1 but i... (answered by Alan3354,jsmallt9)
Please help me rationalize the denominator: 3square root symbol (this is cube root) -3... (answered by edjones)
√3:(16/27) The cube root of sixteen over twenty-seven Is the answer for this... (answered by aaronwiz)
I dont know how to evaluate this problem because of the cube root. Someone please help... (answered by stanbon)
I need to simplify the cube root of -60 over the cube root of 120. I think it is the... (answered by Edwin McCravy)
I don't know if I wrote this problem correct, but here goes: Simplify the cube root. 3... (answered by jim_thompson5910)
the value of 2 cube root 4 + 7 cube root 32 - cube root 500... (answered by mananth)
Please walk me through each step in solving this problem: Simplify by collecting... (answered by jim_thompson5910)
Hello. The problem is -3 (cube root, I dont know how to type the sign) -27. I have come... (answered by Nate)