Cubes and Cube Roots Class 8 Notes given here come in an easy to understand format and students can quickly go through all the topics given in chapter 7. The notes will help students to understand and remember the concepts better and prepare well for the exams. Notably, some of the topics found in the notes include;
- What is a Cube?
- Properties of Cube Numbers
- Interesting Patterns Of Cube Number
- Cube Roots
- Methods To Find A Cube Root
- Important Questions
What is a Cube?
A cube is a three-dimensional figure consisting of six square sides which are all equal. The square faces are joined along their edges. Similarly, a cuboid whose height, length and breadth are equal in measurement is termed as a cube.
Perfect cubes or Cube number is a number which is the product of three same numbers. For example, the cube number of 2 will be 2 x 2 x 2 = 8. Therefore, 8 is a cube number.
Properties of Cube Numbers
- Even number will always have an even cube number.
Example: 6 = 216, 12 = 1728, etc.
- An odd number will always have an odd cube number.
Example: 3 = 27, 9 = 729, etc.
- A cube number having x at its one’s digit or unit’s place will always have the same digit at the end. It can be seen in the table below:
Interesting Patterns Of Cube Number
- Adding consecutive odd numbers will generate cube number
1 = 1 = 13
3 + 5 = 8 = 23
7 + 9 + 11 = 27 = 32
- Prime factors and cubes
A cube number will have a prime factor in a pair of 3.
For example, 43 = 2 x 2 x 2 x 2 x 2 x 2 = 23 x 33
When a number multiplies itself three times to give some cubic value it is known as a cube root. It is the inverse operation of finding a cube. Usually, the symbol ∛ is used to represent a cube-root. An example of cube root includes: ∛8 = 2, ∛216 = 6.
Methods To Find A Cube Root
Prime Factorisation Method
There are various steps that need to be followed.
- Step 1: Calculate the prime factors of the cube number.
- Step 2: Make groups of 3 for common digits.
- Step 3: Group of 3 should be replaced by a single digit.
- Step 4: Cube root is given by the product of single digits.
2. Estimation Method
- Step1: Form groups of three and you have to start from the right side.
- Step 2: The first group will give the unit’s digit of the desired cube root.
- Step 3: Take the other group and let it be mno. Find, a3 < mno < b3. We take the one’s place, of the smaller number a3 as the ten’s place of the required cube root.
- Step 4: The numbers that are found in step 2 and step 3 will reveal the final outcome.
- Find the cube root of given numbers by prime factorisation method.
i. 84 ii. 612 iii. 12846 iv. 37000
- 216 is a perfect cube. Can you tell or guess its cube root without factorisation?
- Which of the numbers are not perfect cubes:
i.100 ii. 1000 iii. 128
- Deepak makes a cuboid having sides of 4cm, 2cm and 6cm. How many cuboids he will need to form a cube?