Question

Find the cube root of $24389$ by estimation method.

• A. $27$
• B. $31$
• C. $29$
• D. $33$

Answer 1

The correct option is C $29$

Step $I$: Form groups of $3$ starting from right most digit of $24389$, i.e. $\overline{24}\overline{389}$.

Then, the two groups are $24$ and $389.$

Here, $24$ has $2$ digit and $389$ has $3$ digit.

Step $II$: Take $389$.

Digit in unit place $=9$.

Therefore, we take one's place of required cube root as $9$ ....[Since, $9^3=729$].

Step $III$: Now, take the other group $24$.

We know, $3^3=27$ and $2^3=84$.

Here, the smallest number among $3$ and $2$ is $2$.

Therefore, we take $2$ as ten's place.

$\therefore \sqrt[3]{324389}=29$.

Hence, option $C$ is correct.