Question

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

$8.6$

Answer 1

Step: Find the cube root of $8.6$

$x$	$\sqrt[3]{3x}$	$\sqrt[3]{310x}$	$\sqrt[3]{3100x}$
$10$	$2.154$	$4.642$	$10$
$86$	$4.414$	$9.510$	$20.49$

$\therefore \sqrt[3]{38.6}=\sqrt[3]{3\frac{86}{10}}$

$=\frac{\sqrt[3]{386}}{\sqrt[3]{310}}[\therefore \sqrt[3]{3\frac{a}{b}}=\frac{\sqrt[3]{3a}}{\sqrt[3]{3b}}]$

From the cube root table,

$\sqrt[3]{386}=4.414$ and $\sqrt[3]{310}=2.154$

$\therefore \frac{\sqrt[3]{386}}{\sqrt[3]{310}}=\frac{4.414}{2.154}$

$=2.049$

Hence, the cube root of $8.6$ is $2.049$.