Making use of the cube root table, find the cubes root of the following (correct to three decimal places)
732

Given: 

732

To find: 

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

Solution:

$\sqrt[3]{732}=\sqrt[3]{73.2 \times 10}$

$=\sqrt[3]{73.2} \times \sqrt[3]{10}$

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

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

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

The difference in the values $=4.198-4.179$

$=0.019$

This implies,

For the difference of $0.2$,

The difference in the values $=0.019 \times 0.2$

$=0.0038$

$=0.004$

Therefore,

$\sqrt[3]{73.2}=4.179+0.004$

$=4.183$

$\sqrt[3]{10}=2.154$

$\sqrt[3]{732} =\sqrt[3]{73.2} \times \sqrt[3]{10}$

$=2.154 \times 4.183$

$=9.010182$

$=9.010$

Tutorialspoint

Updated on: 10-Oct-2022

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