NCERT Solutions for Chapter: Cubes and Cube Roots, Exercise 1: Exercise

What is the value of $\sqrt[3]{64}-\frac{1}{\sqrt[3]{64}}?$

If $x=\frac{\sqrt[3]{\sqrt{625}[\sqrt[3]{8}+\sqrt[3]{27}]}}{\sqrt{64}-\sqrt{9}}$, then find $x^3+\frac{1}{x^3}+\sqrt[\frac{1}{3}]{8}$

The breadth of a cuboid is twice the height of the cuboid and the length is thrice of its breadth. If the volume of the cuboid is $2592 {\mathrm{cm}}^3$, find the length of the cuboid.

What is the least positive integer by which $4500$ should be divided so that the quotient is a perfect cube?

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

$1730$

Find the cube root of the following number.

$970299$

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

$1400$

Perfect cubes of odd numbers may not be always odd.