Cube and cube roots -2

Math Problems

1. The smallest number by which $686$ should be divided to make it a perfect cube is:

   Solution:

   The prime factorization of $686$ gives $2*7^3$. To make it a perfect cube, it should be divided by $2$. Hence, the smallest number by which $686$ should be divided to make it a perfect cube is $2$.

2. Find cube root of:

   1. $1\frac{127}{216}$
   2. $9.261$

   Solution:

   1. The cube root of $1\frac{127}{216}$ is $1\frac{1}{3}$.
   2. The cube root of $9.261$ is approximately $2.1$.

3. Difference of two perfect cubes is $387$. If the cube root of the greater of two numbers is $8$, find the cube root of smaller number.

   Solution:

   If the cube root of the greater number is $8$, then the greater number is $8^3=512$. Hence, the smaller number is $512-387=125$. The cube root of $125$ is $5$. So, the cube root of the smaller number is $5$.