Question

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

$133100$

Answer 1

Step: Find the cube root of $133100$

$x$	$\sqrt[3]{3x}$	$\sqrt[3]{310x}$	$\sqrt[3]{3100x}$
$10$	$2.154$	$4.642$	$10$

$\because 133100=11\times 11\times 11\times 100$

$\therefore \sqrt[3]{3133100}=\sqrt[3]{311\times 11\times 11\times 100}$

$\Rightarrow \sqrt[3]{3133100}=11\times \sqrt[3]{3100}$

(From the table,$\sqrt[3]{3100}=4.642)$

$\sqrt[3]{3133100}=11\times 4.642$

$=51.062$

Hence, the cube root of $133100$ is $\mathrm{51.062.}$