Question

Find the cube root of each of the following integers :

$\left(iv\right)-753571$

Answer 1

Step: Find the cube root of $-753571$

$\begin{array}{cc}\text{7}& \text{753571}\\ \text{7}& \text{107653}\\ \text{7}& \text{15379}\\ \text{13}& \text{2197}\\ \text{13}& \text{169}\\ \text{13}& \text{13}\\ & \text{1}\end{array}$

$\sqrt[3]{3-753571}=-\sqrt[3]{3753571}[\because \sqrt[3]{3-x}=-\sqrt[3]{3x}]$

Resolving $753571$ into prime factors
$753571=7\times 7\times 7\times 13\times 13\times 13$

Now, by grouping the factors into the triplets of equal factors, we get,
$753571=(7\times 7\times 7)\times (13\times 13\times 13)$

$\therefore \sqrt[3]{3753571}=7\times 13$
$=91$
$\therefore \sqrt[3]{3-753571}=-91$

Hence, the cube root of $-753571$ is $-91$ .