Question

cube root of 27 into 2744​

Answer 1

$\textbf{To find:}$

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

$\textbf{Solution:}$

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

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

$27=3^3$

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

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

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

$\implies\sqrt[3]{2744}=14$

$\text{Now,}$

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

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

$=3{\times}14$

$=42$

$\therefore\bf\sqrt[3]{27{\times}2744}=12$

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Answer 2

Cube root of 27×2744=12

Explanation:

First we have to find cube root of 27 by prime factorization method.

Cube root of 27 is equal to 3

Now,cube root of 2744 is equal to 14

Cube root of 27 ×2744

=cube root of 27 ×cube root of 2744

= 3×14

= 42

Therefore cube root of 27×2744=12

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