Making use of the cube root table, find the cubes root of the following (correct to three decimal places)
7342

Given: 

7342

To find: 

We have to find the cube root of the given number correct to three decimal places using cube root table.

Solution:

$\sqrt[3]{7342}=\sqrt[3]{73.42 \times 100}$

$=\sqrt[3]{73.42} \times \sqrt[3]{100}$

$\sqrt[3]{73}=4.179$

$\sqrt[3]{74}=4.198$

For the difference $(74-73)=1$,

The difference in the values $=4.198-4.179$

$=0.019$

This implies,

For the difference of $0.42$,

The difference in the values $=0.019 \times 0.42$

$=0.00798$

$=0.008$

Therefore,

$\sqrt[3]{73.42}=4.179+0.008$

$=4.187$

$\sqrt[3]{100}=4.642$

$\sqrt[3]{7342} =\sqrt[3]{73.42} \times \sqrt[3]{100}$

$=4.642 \times 4.187$

$=19.436054$

$=19.436$

Tutorialspoint

Updated on: 10-Oct-2022

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