Question

Evaluate the following cube root
$\sqrt[3]{{ - 2\dfrac{{10}}{{27}}}}$

Answer 1

Hint:- In this question we have given $\sqrt[3]{{ - 2\dfrac{{10}}{{27}}}}$ So the key concept is that first simplify the inner part of the cube root by using the concept of fraction and then apply the cube root.

Complete step-by-step answer:
Now consider the given expression
$
   \Rightarrow \sqrt[3]{{ - 2\dfrac{{10}}{{27}}}} \\
   \Rightarrow \sqrt[3]{{ - \dfrac{{64}}{{27}}}} \\
   \Rightarrow \sqrt[3]{{ - {{\left( {\dfrac{4}{3}} \right)}^3}}} \\
   \Rightarrow \sqrt[3]{{( - 1) \times {{\left( {\dfrac{4}{3}} \right)}^3}}} \\
$ ………… (1)
Now taken $\dfrac{4}{3}$ outside of cube root from equation (1) we get,
$ \Rightarrow \dfrac{4}{3} \times \sqrt[3]{{ - 1}}$ ………. (2)
And we can write $ - 1 = {\left( { - 1} \right)^3}$ in equation (2) we get,
$
   \Rightarrow \dfrac{4}{3} \times \sqrt[3]{{{{\left( { - 1} \right)}^3}}} \\
   \Rightarrow \dfrac{4}{3} \times ( - 1) \\
   \Rightarrow - \dfrac{4}{3} \\
$
 Hence the answer is $ - \dfrac{4}{3}$ .
Note :- Whenever we face such types of problems the key concept is to simplify the given expression in-to-out which means that first solve the inner part and then simplify the cube root part of the expression to get the right answer.