Question

Find the cube root of \[39304\] by estimation method.
A. 24
B. 44
C. 34
D. 54

Answer 1

Hint: Estimating cube root of a number we follows the subsequent steps:
Step I: First we take any cube number and begin making a group of three digits ranging from the rightmost digit of the quantity.
Step II: The unit digit of the primary group will decide the unit digit of the cube root.
Step III: Find the cube of the number between which the second group lie.
Step IV: We take one's place of the smaller number as the ten's place of the specified cube root.

Complete step by step solution:
Step I: : First we take any cube number and begin making a group of three digits ranging from the rightmost digit of the quantity. Form groups of three ranging from right most digit of \[39304\] ,
Then, the two groups are \[39\] and \[304\] .
Here, \[39\] has two digits and \[304\] has three digits.

Step II: The unit digit of the primary group will decide the unit digit of the cube root.
Take \[304\] .
Digit in unit place is \[4\] .
Therefore, we take one's place of required root as \[4\] ....[Since, ${4^3} = 64$] .

Step III: Now, take the opposite group \[39\] .
We know, ${3^3} = 27$ and ${4^3} = 64$.
Here, the tiniest number among $3$ and \[4\] is $3$.
Therefore, we take $3$ as ten's place.
 \[\therefore 39304 \simeq {34^3}\]
Hence, option $C$ is correct.
So, the correct answer is “Option B”.

Note: Questions similar in nature as that of above can be approached in a similar manner and we can solve it easily. Cube root of a number could be a number that when multiplied three times by itself gives that number.
The symbol $\sqrt[3] {{\text{ }}}$ denotes cube root.