Making use of the cube root table, find the cube root 34.2 - Vidyadip

Question

Making use of the cube root table, find the cube root 34.2

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Answer

The number 34.2 could be written as $\frac{342}{10}.$
Now
$\sqrt[3]{34.2}$
$=\sqrt[3]{\frac{342}{10}}$
$=\frac{\sqrt[3]{342}}{\sqrt[3]{10}}$
Also
340 < 342 < 350
$\Rightarrow\sqrt[3]{340}<\sqrt[3]{342}<\sqrt[3]{350}$
From the cube root table, we have:
$\sqrt[3]{340}=6.980$ and $\sqrt[3]{350}=7.047$
$\therefore$ For the difference (350 - 340), i.e., 10, the difference in values
= 7.047 - 6.980 = 0.067.
$\therefore$ For the difference (342 - 340), i.e., 2, the difference in values
$=\frac{0.067}{10}\times2=0.013$ (upto three decimal places)
$\therefore\sqrt[3]{342}$
$=3.980+0.0134=6.993$ (upto three decimal places)
From the cube root table, we also have:
$\sqrt[3]{10}=2.154$
$\therefore\sqrt[3]{34.2}$
$=\frac{\sqrt[3]{342}}{\sqrt[3]{10}}$
$=3.246$
Thus, the required cube root is 3.246.

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