Making use of the cube root table, find the cubes root of the following (correct to three decimal places)
37800

Given: 

37800

To find: 

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

Solution:

$\sqrt[3]{37800}=\sqrt[3]{37.8 \times 1000}$

$=\sqrt[3]{37.8} \times 10$

$\sqrt[3]{37}=3.332$

$\sqrt[3]{38}=3.362$

For the difference $(38-37)=1$,

The difference in the values $=3.362-3.332$

$=0.030$

This implies,

For the difference of $0.8$,

The difference in the values $=0.030 \times 0.8$

$=0.0240$

$=0.024$

Therefore,

$\sqrt[3]{37.8}=3.332+0.024$

$=3.356$

$\sqrt[3]{37800} =\sqrt[3]{37.8} \times 10$

$=3.356 \times 10$

$=33.56$

Tutorialspoint

Updated on: 10-Oct-2022

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