Question

Imani and Yasmine both simplified the following radical expression, which student is correct? What mistake was made by the student that was incorrect? Explain your reasoning.

Answer 1

Given:

$\sqrt[]{56a^3b}$

$\begin{gathered} \sqrt[]{56a^3b}=\sqrt[]{2\times2\times2\times7\times a^3\times b} \\ \sqrt[]{56a^3b}=2a\sqrt[]{2\times7\times a\times b} \\ \sqrt[]{56a^3b}=2a\sqrt[]{14ab} \end{gathered}$

Imani's work is correct.

Yasmine's mistake is she had taken the cube root of the expression but the given is square root.