Question

Which one of the following is the greatest?
[a] 2
[b] $\sqrt[3]{3}$
[c] $\sqrt[3]{4}$
[d] $\sqrt[3]{2}$

Answer 1

Hint: Compare option [a] with option [b]. Choose the greater one and compare it with option [c]. Now again choose the greater one and compare it with option [d]. Hence find the greatest among [a],[b], [c] and [d]. Use the fact that $a>b$ if and only if ${{a}^{3}}>{{b}^{3}}$.

Complete step-by-step answer:
Comparing option [a] with option [b]
We have ${{2}^{3}}=8$ and ${{\left( \sqrt[3]{3} \right)}^{3}}=3$
Since 8>3, we have $2>\sqrt[3]{3}$.
Hence among option [a] and option [b], option [a] is greater.
Comparing option [a] with option [c].
We have ${{2}^{3}}=8$ and ${{\left( \sqrt[3]{4} \right)}^{3}}=4$
Since 8>4, we have $2>\sqrt[3]{4}$.
Hence among option [a] and option [c], option [a] is greater.
Comparing option [a] with option [d]
We have ${{2}^{3}}=8$ and ${{\left( \sqrt[3]{2} \right)}^{3}}=2$
Since 8>2, we have $2>\sqrt[3]{2}$.
Hence among option [a] and option [d], option [a] is greater.
Hence option [a] is the greatest.
Hence [a] is correct.

Note: In these types of questions, we have to solve the question sequentially. If we follow randomly, then we have to do 24 comparisons, but if we follow sequentially, then only three comparisons are sufficient.
Hence the task is reduced significantly if we follow the sequential order.