R. D. Sharma Solutions for Chapter: Cubes and Cube Roots, Exercise 1: EXERCISE

Observe the following pattern:

                         $1^3=1$

                $1^3+2^3=(1+2{)}^2$

       $1^3+2^3+3^3=(1+2+3{)}^2$

Write the next three rows and calculate the value of $1^3+2^3+3^3+\dots +9^3+{10}^3$ by the above pattern.

Which of the following are cubes of even natural numbers?

$216, 512, 729, 1000, 3375, 13824$

Which of the following are cubes of odd natural numbers?

$125, 343, 1728, 4096, 32768, 6859$

What happens to the cube of a number if the number is multiplied by

$5$

Is the given number a perfect cube?

$64$.

Is the following number a perfect cube?

$216$

Check whether the given number is not a perfect cube?

$243$.

Check whether the given number is not a perfect cube?

$1728$