RS Aggarwal Solutions Class 8 Maths Chapter 4 Cubes And Cube Roots (Updated For 2021-22)

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RS Aggarwal Solutions Class 8 Maths Chapter 4 Cubes And Cube Roots

RS Aggarwal Solutions Class 8 Maths Chapter 4 Cubes And Cube Roots – Overview

There are various exercises in the RS Aggarwal Solutions Class 8 Maths Chapter 4 that will discuss the concepts related to cube and cube roots. 

• Cubes

Cube numbers or perfect cubes are the numbers obtained when a number is multiplied three times by itself.

For example: 1, 8, 27, …, etc.

The cube of the natural number m is denoted by m3 and it is expressed as m3 = m × m × m.

Thus, 13 = 1 × 1 × 1 = 1

23 = 2 × 2 × 2 = 8

33 = 3 × 3 × 3 = 27, and so on.

• Patterns

The number is said to be a perfect cube, if in the prime factorization of any number, each prime factor occurs three times. 

For example, 216 = 2 × 2 × 2 × 3 × 3 × 3 = 23 × 33 = (2 × 3)3 = 63 which is a perfect cube.

• Smallest Multiple That’s a Perfect Cube

We find the smallest natural number by which a number is multiplied or divided to make it a perfect cube.

• Cube Root

The inverse operation of finding the cube is called a cube root.

23 = 8 ⇒ 2 is the cube root of 8.

The symbol ∛ denotes the cube root. Thus,∛8 = 2.

• Cube Root Using Prime Factorisation Method

1. To find the cube root using prime factorisation method, long division method or the manual square method can be used. 
2. Create a pair of three digits from the back to the centre, find a number whose cube root is less than or equal to that number.
3. Then, deduct the obtained number from the specified number and enter the second number. Then, find the multiplication factor for the further phase in the long division system, which results from the multiplication of the first number obtained.
4. Continue the process mentioned above to find the cube root of a number. You can use this method when the number in question is not the perfect cube number. 

• Steps To Find Cube Root Of A Cube Number

1. Get a given number. Start making groups of three digits starting from the digit on the right side of the number.

2. The first group will give the appropriate cube root (unit) digit.

3. Then take the next party. Find the nearest cube numbers in which this group is found. Take one’s place of the smaller number as ten’s place of the required cube root.

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