Question

Find the cube root of each of the following Rational numbers:

i) $-\frac{125}{729}$

Answer 1

Step: Find the cube root of $-\frac{125}{729}$

Cube root of $-\frac{125}{729}=\sqrt[3]{3-\frac{125}{729}}$

$\sqrt[3]{3\frac{125}{729}}=\frac{\sqrt[3]{3-125}}{\sqrt[3]{3729}}$

$[\because \sqrt[3]{3\frac{a}{b}}=\frac{\sqrt[3]{3a}}{\sqrt[3]{3b}}]$

$=\frac{-\sqrt[3]{3125}}{\sqrt[3]{3729}}$

$[\because \sqrt[3]{3-a}]=-\sqrt[3]{3a}]$

$=\frac{-\sqrt[3]{35\times 5\times 5}}{\sqrt[3]{39\times 9\times 9}}$

$=-\frac{5}{9}$

Hence, the cube root of $-\frac{125}{729}$
is $-\frac{5}{9}$