Answer:
use an appropriate calculator
Step-by-step explanation:
You didn't ask the value; you only asked how to find the value. Here is an answer for that question.
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If your calculator does not have a cube-root function, you can use a 1/3 power:
[tex]\sqrt[3]{219}=219^{1/3}[/tex]
Alternatively, you can use logarithms:
[tex]\sqrt[3]{219}=10^{\left(\frac{1}{3}\log{219}\right)}[/tex]
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The Google calculator recognizes the cube root( ) function as shown in the attachment.
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Since you know 6^3 = 216, you know the cube root of 219 is only a little more than 6. A couple of iterations of ...
x' = (2/3)x +73/x^2
can refine your first guess of x=6 to 8 decimal places of accuracy, where x' is the next "guess". One more iteration will give the cube root to the accuracy displayed by most calculators.
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In the above iteration formula, the value 73 is 219/3. This same sort of iterative technique can be used for any cube root. It calculates the next guess as the weighted average: 2/3 of the previous guess and 1/3 of the number divided by the square of the guess. Once you're in the ballpark, it will double the number of accurate decimal digits on each iteration.
