Question
Making use of the cube root table, find the cube root 37800
✓
Answer
$37800 = 2^3 × 3^3 × 175$
$\Rightarrow \sqrt[3]{37800}$
$=\sqrt[3]{2^3\times3^3\times175}$
$=6\times\sqrt[3]{175}$
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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