Question
Making use of the cube root table, find the cube root $37800$
✓
Answer
$37800=2^3 \times 3^3 \times 175$
$\Rightarrow \sqrt[3]{37800}$
$=\sqrt[3]{2^3\times3^3\times175}$
$=6\times\sqrt[3]{175}$
Also
$170 < 175 < 180$
$ \Rightarrow\sqrt[3]{170}<\sqrt[3]{175}<\sqrt[3]{180}$
From cube root table, we have:
$\sqrt[3]{170}=5.540 $ and $\sqrt[3]{180}=5.646$
$\therefore$ For the difference $(180 - 170)$, i.e., $10$,
the difference in values $= 5.646 - 5.540 = 0.106$
$\therefore$ For the difference of $(175 - 170)$, i.e., $5$,
the difference in values
$=\frac{0.106}{10}\times5=0.053$
$\therefore\sqrt[3]{175}$ $=5.540+0.053$
$=5.593$
Now
$37800$
$= 6\times\sqrt[3]{175}=6\times5.593=33.558$
Thus, the required cube root is $33.558$.
$\Rightarrow \sqrt[3]{37800}$
$=\sqrt[3]{2^3\times3^3\times175}$
$=6\times\sqrt[3]{175}$
Also
$170 < 175 < 180$
$ \Rightarrow\sqrt[3]{170}<\sqrt[3]{175}<\sqrt[3]{180}$
From cube root table, we have:
$\sqrt[3]{170}=5.540 $ and $\sqrt[3]{180}=5.646$
$\therefore$ For the difference $(180 - 170)$, i.e., $10$,
the difference in values $= 5.646 - 5.540 = 0.106$
$\therefore$ For the difference of $(175 - 170)$, i.e., $5$,
the difference in values
$=\frac{0.106}{10}\times5=0.053$
$\therefore\sqrt[3]{175}$ $=5.540+0.053$
$=5.593$
Now
$37800$
$= 6\times\sqrt[3]{175}=6\times5.593=33.558$
Thus, the required cube root is $33.558$.
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