![First of all we will factorise 1728 (as shown in the figure).
Now we will write all the prime factors obtained as - 1728 =
2 Ć 2 Ć 2 Ć 2 Ć 2 Ć 2 Ć 3 Ć 3 Ć 3
Then we will make groups of three same numbers and write
one common of them as -
1728 = [2 Ć 2 Ć 2] Ć [2 Ć 2 Ć 2] Ć [3 Ć 3 Ć 3]
= 2 Ć 2 Ć 3
= 12
Therefore, cube root of 1728 is 12.
Find the cube root of
1728.](https://image.slidesharecdn.com/ch4cubesandcuberoots-231003060749-a9c7b233/85/Ch-4-Cubes-and-Cube-roots-ppt-22-320.jpg)
![First of all we will factorise 970299 (as shown in the figure).
Now we will write all the prime factors obtained as -
970299 = 3 Ć 3 Ć 3 Ć 3 Ć 3 Ć 3 Ć 11 Ć 11 Ć 11
Then we will make groups of three same numbers and write
one
common of them as -
1728 = [3 Ć 3 Ć 3] Ć [3 Ć 3 Ć 3] Ć [11 Ć 11 Ć 11]
= 3 Ć 3 Ć 11
= 99
Therefore, cube root of 970299 is 99.
Find the cube root of 970299.](https://image.slidesharecdn.com/ch4cubesandcuberoots-231003060749-a9c7b233/85/Ch-4-Cubes-and-Cube-roots-ppt-24-320.jpg)
Ch 4 Cubes and Cube roots.ppt
- 1. Ch 4 Cubes and Cube roots ļ§ Perfect cubes ļ§ Properties of cube numbers ļ§ Prime factorisation to find cube root ļ§ Imperfect cube to perfect cube ļ§ Cube root of negative numbers ļ§ Cube root of decimals ļ§ Cube root of rational numbers
- 2. CUBE NUMBERS AND ITS PROPERTIES
- 3. Property 1 If a number end with 1, then its cube will also end with 1 Example: Numbers Oneās Place Rule Answer 51 1 number end with 1 Cube of 51 will end with 1 121 1 number end with 1 Cube of 121 will end with 1 191 1 number end with 1 Cube of 191 will end with 1 23571 1 number end with 1 Cube of 23751 will end with 1
- 4. Property 2 If a number ends with 0 , 1 , 4 , 5 , 6 and 9 , then its cube will end with same number For Example: Numbers Oneās Place Rule Answer 11 1 number ends with 0 , 1 , 4 , 5 , 6 and 9 Cube of 11 will end with 1 14 4 number ends with 0 , 1 , 4 , 5 , 6 and 9 Cube of 14 will end with 4 15 5 number ends with 0 , 1 , 4 , 5 , 6 and 9 Cube of 15 will end with 5 16 6 number ends with 0 , 1 , 4 , 5 , 6 and 9 Cube of 16 will end with 6 20 0 number ends with 0 , 1 , 4 , 5 , 6 and 9 Cube of 20 will end with 0 19 9 number ends with 0 , 1 , 4 , 5 , 6 and 9 Cube of 19 will end with 9
- 5. Property 3 If a number end with 2, then its cube will end with 8 If a number end with 8, then its cube will end with 2 For Example: Numbers Oneās place Rule Answer 12 2 Number ends with 2 Cube of 12 will end with 8 18 8 Number ends with 8 Cube of 8 will end with 2
- 6. Property 4 If a number end with 3, then its cube will end with 7 If a number end with 7, then its cube will end with 3 For Example: Numbers Ones place Rule Answer 13 3 number end with 3 cube of 13 will end with 7 17 7 number end with 7 cube of 17 will end with 3
- 7. Property 5 Observe the following table Cubes of an even numbers are all even numbers Cubes of odd numbers are all odd numbers Number Square 2 8 4 64 6 216 8 512 10 1000 Number Square 1 1 3 27 5 125 7 343 9 729
- 8. Try These By observing the units digits find which of the numbers cannot be a perfect cube 2321 , 1335 , 20949 , 30550 , 21368 , 4173.
- 10. A perfect cube is a number that is the cube of an integer. For example, 125 is a perfect cube since 125 = 5 Ć 5 Ć 5 = 53. Some other examples of perfect cubes are 1, 8, 27, 64, 125, 216, 343, ā¦ Perfect Cube
- 12. There are many numbers which are not perfect cubes and we cannot find the cube root of such numbers using the prime factorisation and estimation method. Let us find the cube root of 150 here. Clearly, 150 is not a perfect cube. It will be around 5.31. So the cube root value of non perfect cubes are in decimals or not integers. Non-Perfect Cube
- 14. In mathematics, a cube root of a number x is a number y such that yĀ³ = x. All nonzero real numbers, have exactly one real cube root and a pair of complex conjugate cube roots, and all nonzero complex numbers have three distinct complex cube roots. Cube Root
- 15. 3 27 CUBE 3 ā 3 ā 3 CUBE ROOT
- 18. Prime Factorisation ļ§ Prime factorization of any given number is to breakdown the number into its factors until all of its factors are prime numbers. This can be achieved by dividing the given number from smallest prime number and continue it until all its factors are prime.
- 19. Finding Cube Root by Prime Factorisation
- 20. In order of finding cube root by prime factorization we use the following steps : Step I : Obtain the given number. Step II : Resolve it into prime factors. Step III : Group the factors in 3 in such a way that each number of the group is same. Step IV : Take one factor from each group. Step V : Find the product of the factors obtained in step IV. This product is the required cube root. Steps to Find Cube Root by Prime Factorisation
- 22. First of all we will factorise 1728 (as shown in the figure). Now we will write all the prime factors obtained as - 1728 = 2 Ć 2 Ć 2 Ć 2 Ć 2 Ć 2 Ć 3 Ć 3 Ć 3 Then we will make groups of three same numbers and write one common of them as - 1728 = [2 Ć 2 Ć 2] Ć [2 Ć 2 Ć 2] Ć [3 Ć 3 Ć 3] = 2 Ć 2 Ć 3 = 12 Therefore, cube root of 1728 is 12. Find the cube root of 1728.
- 24. First of all we will factorise 970299 (as shown in the figure). Now we will write all the prime factors obtained as - 970299 = 3 Ć 3 Ć 3 Ć 3 Ć 3 Ć 3 Ć 11 Ć 11 Ć 11 Then we will make groups of three same numbers and write one common of them as - 1728 = [3 Ć 3 Ć 3] Ć [3 Ć 3 Ć 3] Ć [11 Ć 11 Ć 11] = 3 Ć 3 Ć 11 = 99 Therefore, cube root of 970299 is 99. Find the cube root of 970299.