Question
Making use of the cube root table, find the cube root $8.65$
✓
Answer
The number $8.65$ can 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 $(870 - 860),$ i.e., $10,$ the difference in values
$= 9.546 - 9.510 = 0.036$
$\therefore$ For the difference of $(865 - 860)$, i.e., $5$, the difference in values
$=\frac{0.036}{10}\times5=0.018$ (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 $2.053$.
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 $(870 - 860),$ i.e., $10,$ the difference in values
$= 9.546 - 9.510 = 0.036$
$\therefore$ For the difference of $(865 - 860)$, i.e., $5$, the difference in values
$=\frac{0.036}{10}\times5=0.018$ (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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