# Evaluate the following cube root

$\sqrt[3]{{ - 2\dfrac{{10}}{{27}}}}$

Answer

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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.

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.

Last updated date: 18th Sep 2023

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