Question

Find the estimated cube root of 1601613.

• A. 117
• B. 127
• C. 137
• D. 147

Answer 1

The correct option is A 117

Step 1: Start making the number into 2 groups, with 3 digits from the unit place as 1${}^{\text{st}}$ group and remaining 4 digits as 2${}^{\text{nd}}$ group
i.e. 1601 613
Second group First group

Step 2: First group i.e 613 will give us the units digit of the cube root. As 613 ends with 3, so, the units place of the cube root will be 7.

Step 3: Now, take second group i.e. 1601
We know that ${11}^3\left(1331\right)<1601<{12}^3\left(1728\right)$
As the smallest number is 11, it becomes the remaining part of the required cube root
$\therefore$$\sqrt[3]{31601613}=117$