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Making use of the cube root table, find the cubes root of the following (correct to three decimal places)
5112
Given:
5112
To find:
We have to find the cube root of the given number correct to three decimal places using cube root table.
Solution:
$\sqrt[3]{5112}=\sqrt[3]{2 \times 2 \times 2 \times 639}$
$=2 \sqrt[3]{639}$
$=2 \sqrt[3]{63.9 \times 10}$
$=2 \times \sqrt[3]{63.9} \times \sqrt[3]{10}$
$\sqrt[3]{63}=3.979$
$\sqrt[3]{64}=4.000$
For the difference $(64-63)=1$,
The difference in the values $=4.000-3.979$
$=0.021$
This implies,
For the difference of $0.9$,
The difference in the values $=0.021 \times 0.9$
$=0.0189$
$=0.019$
Therefore,
$\sqrt[3]{63.9}=3.979+0.019$
$=3.998$
$\sqrt[3]{5112}=2 \times \sqrt[3]{10} \times \sqrt[3]{63.9}$
$=2 \times 2.154 \times 3.998$
$=17.223384$
$=17.223$
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