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,

$\sqrt[3]{63.9}=3.979+0.019$

$=3.998$

$\sqrt[3]{5112}=2 \times \sqrt[3]{10} \times \sqrt[3]{63.9}$

$=2 \times 2.154 \times 3.998$

$=17.223384$

$=17.223$

Tutorialspoint

Updated on: 10-Oct-2022

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