S Purkayastha Solutions for Chapter: Cubes and Cube Roots, Exercise 4: MENTAL MATHS

If $a$ divides $b$, then $a^3$ divides $b^3$

If $a^2$ ends in $4$, then $a^3$ ends in $8$

If $a^2$ ends in $5$, then $a^3$ ends in $5$

If $a$ and $b$ are integers such that $a^2>b^2\text{, then }{a}^3>b^3$.

No perfect cube can end with exactly two zeroes.

Observe the pattern.

$1^3=1,1^3+2^3=9=(1+2{)}^2,1^3+2^3+3^3=36=(1+2+3{)}^2$

Write the next three rows and calculate the value.

Solve, $1^3+2^3+3^3+\dots +9^3+{10}^3$ using the above pattern.

Three numbers are in the ratio as $2:3:4$. The sum of their cubes is $33957$. Find the numbers.

Which is bigger number ${\left({10}^3\right)}^3\text{ or }(10{)}^{\left(3\right)}$ ?