SOLUTION: Simplify. 3√1000 I have gotten the answer 333.3. Is that right?

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Question 371971: Simplify. 3√1000
I have gotten the answer 333.3. Is that right?
Found 2 solutions by Fombitz, jsmallt9:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
No, 1000%2F3=333.3
You're looking for the cube root of 1000.
What number multiplied by itself three times equals 1000.
N%5E3=1000
N=root%283%2C1000%29
N=10
because,
10%2A10%2A10=1000

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
3sqrt%281000%29
Simplify does not mean find a decimal approximation. Simplifying an expression with a square root means reduce the square root, if possible. Reducing a square root is done by finding perfect square factors, if any, of the radicand (the expression within the radical). So we are looking for perfect square factors of 1000. I hope it is easy to see that 100 is a perfect square and it is a factor of 1000:
3sqrt%28100%2A10%29
Next we use a property of radicals, root%28a%2C+p%2Aq%29+=+root%28a%2C+p%29+%2A+root%28a%2C+q%29, to separate the perfect square factor into its own square root:
3sqrt%28100%29%2Asqrt%2810%29
The square root of 100 is 10 so now we have:
3%2A10%2Asqrt%2810%29
or
30sqrt%2810%29
There are no other perfect square factors of 10 (other than 1) so this simplified version of 3sqrt%281000%29. (BTW, the decimal approximation for this is 94.8683298050513800)