I have always used a calculator for determining roots
But I think it would be useful to know how to do this on paper. Are there different procedures for calculating square roots than for cubic roots or does it all use the same principles?
So my question is how does one calculate the root of a number by hand (so to speak)?
Best Answer
A variety of techniques are shown in Wikipedia. Several of them generalize to cube roots. The choice depends on what accuracy you want and how much work you are willing to do. For low accuracy you can often use a table you may have memorized and a small correction. For example, to find $\sqrt{26}$ you can say $26=25\cdot 1.04$, so $\sqrt {26}=\sqrt{25}\sqrt {1.04}\approx 5\cdot 1.02 =5.1$ where we have used $\sqrt {1+x} \approx 1+\frac x2$ for small $x$. The same works for cube roots using $\sqrt[3]{1+x} \approx 1+\frac x3$