SOLUTION: please solve n^3=8000

Algebra ->  Algebra  -> Exponents -> SOLUTION: please solve n^3=8000      Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   


Question 114316: please solve n^3=8000
Found 2 solutions by bucky, scott8148:
Answer by bucky(2097) About Me  (Show Source):
You can put this solution on YOUR website!
One way to begin to solve this equation is to write 8000 in scientific notation. In scientific
notation 8000 = 8 * 10^3 where "*" represents the multiplication operator.
.
Set n^3 equal to this scientific notation for 8000:
.
n%5E3+=+8+%2A+10%5E3
.
Solve for n by taking the cube root of both sides to get:
.
n+=+root%283%2C8%2A10%5E3%29
.
but root%283%2C8%2A10%5E3%29+=+root%283%2C8%29%2Aroot%283%2C10%5E3%29
.
and root%283%2C8%29+=+2 ... and root%283%2C10%5E3%29+=+10
.
so the equation for n reduces to:
.
n+=+root%283%2C8%2A10%5E3%29+=+root%283%2C8%29%2Aroot%283%2C10%5E3%29+=+2%2A10+=+20
.
So the answer is n+=+20
.
Hope this helps you to understand the problem and shows you a calculator-less way to get
the answer.
.

Answer by scott8148(5880) About Me  (Show Source):
You can put this solution on YOUR website!
taking the cube root gives n=20