Question

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

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.
$\Rightarrow \sqrt[3]{{ - 2\dfrac{{10}}{{27}}}} \\ \Rightarrow \sqrt[3]{{ - \dfrac{{64}}{{27}}}} \\ \Rightarrow \sqrt[3]{{ - {{\left( {\dfrac{4}{3}} \right)}^3}}} \\ \Rightarrow \sqrt[3]{{( - 1) \times {{\left( {\dfrac{4}{3}} \right)}^3}}} \\$ ………… (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 $- \dfrac{4}{3}$ .