Cubes and Cube Roots Explained - ICSE Class 8 Maths Chapter 4

Описание: A cube is what you get when you multiply a number by itself three times.

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For example, the cube of five is one hundred twenty-five because five times five times five equals one hundred twenty-five. A number is called a perfect cube if its prime factors can all be grouped into sets of three. In this chapter, you also learn that the cubes of even numbers are always even, while the cubes of odd numbers are always odd. Additionally, the cube of a positive number is positive, and the cube of a negative number is negative.

If a number is not a perfect cube, you can make it one by multiplying or dividing it by a specific small number. To do this, you first find all the prime factors of the number and see which ones do not form a complete group of three. By either adding the missing factors or removing the extra ones through division, you can turn that number into a perfect cube. This process is a great way to practice prime factorization and understand the internal structure of different numbers.

The cube-root is the opposite of a cube; it is the original number that was multiplied by itself to reach a total. You can find the cube-root of a large number by breaking it down into its prime factors and picking one factor from every group of three. This chapter also explains how to handle more complex values, such as negative numbers, products, and fractions. For decimals, the simplest method is to convert them into fractions first and then find the cube-root of the top and bottom numbers separately.

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