Jharne De and Ranjana Kumar Solutions for Chapter: Square and Square Root; Cube and Cube Root, Exercise 6: Test Paper 2

If $a$ divides $b$, then $a^3$ divide $b^3$. Is it true? Give a reason to support your answer.

Find the value of the infinite product given below.

$P=\frac{7}{9}\times \frac{26}{28}\times \frac{63}{65}\times .....\times \frac{k^3-1}{k^3+1}\times .....$

Find the smallest number which can be expressed as a sum of cubes of two numbers in two different ways. Also express the number as a sum of cubes.

If $n^3=4\frac{12}{125}$, then find the value of $n^2-1$.

A gardener wants to plant $500$ plants in such a way that number of plants in each row is equal to the number of rows, but in doing so some plants were left out. Find the number of plants left out in this arrangement.

A decimal number is multiplied by its square. If the product so obtained is $614.125$, find the decimal number.

The sum of two perfect cubes is $854$. If the cube root of smaller number is $5$, then find the cube root of the larger number.

Three numbers are in the ratio $2:3:4$. If the sum of their cubes is $50,688$, then find each number.