SOLUTION: simplify: cube root of 144+cube root of 2/3-5 times cube root of 18 -Tammam Ahmed

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Question 248997: simplify:
cube root of 144+cube root of 2/3-5 times cube root of 18
-Tammam Ahmed
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
root%283%2C+144%29+%2B+root%283%2C+2%2F3%29+-+5root%283%2C+18%29
We cannot add or subtract any of these terms because they are not like terms (yet). But we can simplify them. There are two parts to simplifying radicals:
  • Factoring out perfect powers of the root. (In this case we will be factoring out perfect cubes where possible.)
  • Rationalizing denominators.

The first cube root has a perfect square factor. The middle cube root needs to be rationalized:
root%283%2C+8%2A18%29+%2B+root%283%2C+%282%2F3%29%289%2F9%29%29+-+5root%283%2C+18%29
root%283%2C+8%29%2Aroot%283%2C+18%29+%2B+root%283%2C+18%2F27%29+-+5root%283%2C+18%29
2%2Aroot%283%2C+18%29+%2B+root%283%2C+18%29%2Froot%283%2C+27%29+-+5root%283%2C+18%29
2%2Aroot%283%2C+18%29+%2B+root%283%2C+18%29%2F3+-+5root%283%2C+18%29
Each cube root is now simplified. And they are now like terms! So we can add and subtract them. Of course we need common denominators first:
6%2Aroot%283%2C+18%29%2F3+%2B+root%283%2C+18%29%2F3+-+15root%283%2C+18%29%2F3
-8%2Aroot%283%2C+18%29%2F3
or
%28%28-8%29%2F3%29%2Aroot%283%2C+18%29