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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