PRACTICE QUESTIONS CLASSROOM WING

Find the smallest number which must be subtracted from the following to make it a perfect cube. What is the corresponding cube root?

$833$

Find the smallest number which must be subtracted from the following to make it a perfect cube. What is the corresponding cube root?

$1400$

Find the smallest number which must be subtracted from the following to make it a perfect cube. What is the corresponding cube root?

$1730$

There is a certain number of rows of chairs in a room. The number of chairs in each row is thrice the total number of rows. Find the number of chairs in each row and a number of rows in the room if the number of chairs is $2187$. 

Find the divisor and the quotient, given the dividend is $1035$, the divisor is one-fourth the quotient and the remainder is $11$.

In a five-digit number $1b6a3$, $a$ is the greatest single-digit perfect cube and twice of an exceeds $b$ by $7$. Then the sum of the number and its cube root is _____.  

If $\sqrt[3]{3\left(\sqrt[3]{x}-\frac{1}{\sqrt[3]{x}}\right)}=2,$ then $\sqrt[3]{x}-\frac{1}{\sqrt[3]{x}}=$_____. 

Find the value of $\sqrt[3]{288}\times \sqrt[3]{432}\times \sqrt[3]{648}$.