Question

Find the value of the following cube root.

Answer 1

$\textbf\color{red}{To find:}$

$\sqrt[3]{27{\times}2744}$

$\textbf{Solution:}$

$\text{First we find cube root of 27 and 2744 by factorization method}$

$\begin{gathered}\begin{array}{r|l}3&27\\\cline{2-2}3&9\\\cline{2-2}3&3\\\cline{2-2}&1\\\cline{2-2}\end{array}\end{gathered}$

$\implies\bf\sqrt[3]{27}$

$\begin{gathered}\begin{array}{r|l}2&2744\\\cline{2-2}2&1372\\\cline{2-2}2&686\\\cline{2-2}7&343\\\cline{2-2}7&49\\\cline{2-2}7&7\\\cline{2-2}&1\\\cline{2-2}\end{array}\end{gathered}$

$\color{purple}2744=2^3{\times}3$

$\implies\color{purple}\sqrt[3]{2744}$

$\text\color{red}{Now,}$

$\sqrt[3]{27{\times}2744}$

$=\color{purple}\sqrt[3]{27}{\times}\sqrt[3]{2744}$

$\therefore\bf\color{purple}\sqrt[3]{27{\times}2744}$

Thankyou :)