Question

Find the cube root of each of the following numbers:

(iv) $-729\times -15625$

Answer 1

Step: Find the cube root of $-729\times -15625$

Cube root of $-729\times -15625=\sqrt[3]{3-79\times -15625}$

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

$\therefore \sqrt[3]{3-729\times -15625}$

$=\sqrt[3]{3-729}\times \sqrt[3]{3-15625}$

$=-\sqrt[3]{3729}\times -\sqrt[3]{315625}$ $[\because \sqrt[3]{3-a}=-\sqrt[3]{3a}]$

$\begin{array}{cc}\text{5}& \text{15625}\\ \text{5}& \text{3125}\\ \text{5}& \text{625}\\ \text{5}& \text{125}\\ \text{5}& \text{25}\\ \text{5}& \text{5}\\ & \text{1}\end{array}$


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

$=9\times 5\times 5$

$=225$

Hence, the cube root of $-729\times -15625$
is $225$.