Making use of the cube root table, find the cube root
8.65
The number $8.65$ could be written as $\frac{865}{100}$.
Now
$\sqrt[3]{8.65}=\sqrt[3]{\frac{865}{100}}=\frac{\sqrt[3]{865}}{\sqrt[3]{100}}$
Also
$860<865<870 \Rightarrow \sqrt[3]{860}<\sqrt[3]{865}<\sqrt[3]{870}$
From the cube root table, we have:
$\sqrt[3]{860}=9.510$ and $\sqrt[3]{870}=9.546$
For the difference (870
$=9.546-9.510=0.036$
$\therefore$ For the difference of $(865-860)$, i.e., 5 , the difference in values
$=\frac{0.036}{10} \times 5=0.018$ (upto three decimal places)
$\therefore \sqrt[3]{865}=9.510+0.018=9.528$ (upto three decimal places)
From the cube root table, we also have:
$\sqrt[3]{100}=4.642$
$\therefore \sqrt[3]{8.65}=\frac{\sqrt[3]{865}}{\sqrt[3]{100}}=\frac{9.528}{4.642}=2.053$ (upto three decimal places)
Thus, the required cube root is 2.053.
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