NCERT Solutions for Chapter: Square-Square Root and Cube-Cube Root, Exercise 1: Exercise

Find the length of each side of a cube if its volume is $512 {\mathrm{cm}}^3$.

Three numbers are in the ratio $1:2:3$ and the sum of their cubes is $4500$. Find the numbers.

How many square metres of carpet will be required for a square room of side $6.5 \mathrm{m}$ to be carpeted.

Find three numbers in the ratio $2:3:5,$ the sum of whose squares is $608$.

Three numbers are in the ratio $2:3:4.$ The sum of their cubes is $0.334125.$ Find the numbers.

Put three different numbers in the circles so that when you add the numbers at the end of each line you always get a perfect square.

A three digit perfect square is such that if it is viewed upside down, the number seen is also a perfect square. What is the number? (Hint: The digits $1, 0$ and $8$ stay the same when viewed upside down, whereas $9$ becomes $6$ and $6$ becomes $9$.)

$13$ and $31$ is a strange pair of numbers such that their squares $169$ and $961$ are also mirror images of each other. Can you find two other such pairs?