# RBSE Solutions for Class 8 Maths Chapter 2 Cube and Cube Roots Ex 2.2

RBSE Solutions for Class 8 Maths Chapter 2 Cube and Cube Roots Ex 2.2 is part of RBSE Solutions for Class 8 Maths. Here we have given Rajasthan Board RBSE Class 8 Maths Chapter 2 Cube and Cube Roots Exercise 2.2.

 Board RBSE Textbook SIERT, Rajasthan Class Class 8 Subject Maths Chapter Chapter 2 Chapter Name Cube and Cube Roots Exercise Exercise 2.2 Number of Questions 2 Category RBSE Solutions

## Rajasthan Board RBSE Class 8 Maths Chapter 2 Cube and Cube Roots Ex 2.2

Question 1.
Determine True/False in the given statements.
(i) Every even number(RBSESolutions.com)has even cube.
(ii) A perfect cube does not end with double zero (00).
(iii) No one perfect cube end with 8.
(iv) If square of any number is ending with 5 then its cube is end with 25.
(v) Cube of single digit is also a single digits number.
(vi) Cube of double(RBSESolutions.com)digit number is of 4 to 6 digits.
Solution.
(i) True
(ii) True
(iii) False
(iv) True
(v) False
(vi) True

Question 2.
Find the cube roots of the following numbers by estimate(RBSESolutions.com)and prime factor method. Verify your answer
(i) 64
(ii) 343
(iii) 5832
(iv) 74088
(v) 3375
(vi) 10648
(vii) 46656
(viii) 91125
Solution.
Prime Factorization method
(i) Resolving 64 into Prime factors as follows :

Step I Make groups of three digits, starting from unit place digit as 064
Step II. 1st group is 64. Its unit(RBSESolutions.com)digit is 4 which is obtained only by the cube of a number whose unit digit is 4 (4³ = 64)
Therefore, cube root of 64 is 4.

(ii) Resolving 343 into Prime factors as follows :

Step I. Make group of three digits, starting from unit place digit as 343
Step II. First group is 343. Its(RBSESolutions.com)unit digit is 3 which is obtained only by the cube of a number whose unit digit is 7
(7³ = 343)
∴ Cube root of 343 is 7

(iii) Resolving 5832 into Prime factors as follows :

Step I. Make groups of three digits starting from unit place(RBSESolutions.com)digits as 5 832
Step II. 1st group is 832 and its unit place digit is 2 which is obtained only by the cube a number whose unit digit is 8
(8³ = 512)
So, we get 8 at the unit place digit of the cube root.
Step III. Second group is 5 which is(RBSESolutions.com)greater than cube of 1 and smaller than cube of 2
∴ 1³<5<2³
Therefore, tens place digit is 1 .
Therefore, Cube root of ³√5832 = 18

(iv) Resolving 74088 into Prime factors as follows :

Step I. Make groups of three digits starting from unit place digit as 77 088
Step II. 1st group is 088, its unit digit 8 which is obtained by the cube of 2 i.e. (2³ = 8)
∴ We get 2 at the(RBSESolutions.com)unit places digit of the cube root.
Step III. IInd group is 74
Therefore, 4³ < 74 < 5³
∴ Ten place digit is 4
Therefore. ³√74088 = 42

(v) Resolving 3375 into Prime factors as follows :

Step I. Make groups of three digits, starting from unit place digit as 3 375.
Step II. 1st group is 375 Its unit place digit is 5 which is obtained only by the cube of any number having unit place digit 5
(5³ = 125)
So we get 5 at the unit’s place(RBSESolutions.com)of the cube root.
Step III. IInd group is 3
Which is 1³ < 3 < 2³
Therefore, tens place digit is 1
∴ ³√3375 = 15

(vi) Resolving 10648 into Prime factors as follows :

Step I. Make groups of three digits, starting from unit place digit as 10 648
Step II. 1st group is 648 Its unit place digit is 8 which can be obtained only by the cube of number having unit place digit as 2
(2³ = 8)
Therefore, we get 2 at the unit place digit of the cube root.
Step III. Second(RBSESolutions.com)group is 10
2³ < 10 < 3³
∴ Tens place digit is 2
Therefore, ³√10648 = 22

(vii) Resolving 46656 into Prime factors as follows :

Step I. Make groups of three digits starting from unit place digit as 46 656
Step II. 1st group is 656. Its unit place digit is 6 which is obtained by the cube of any number having unit place digit as 6.
We know that 6³ = 216
Step III. Second(RBSESolutions.com)group is 46
3³<46<4³
∴ Ten place digit is 3
Hence, cube root of 46656 is 36
∴³√46656 = 36

(viii) Resolving 91125 into Prime factors as follows :

Step I. Make digit of three digits, starting from unit place digit 91 125
Step II. 1st group is 125. Its unit place digit is 5 which is obtained only by the cube of any number having unit place digit as 5
(5³ = 125)
Step II. IInd group is 91
Here 4³<91<5³
Therefore,tens(RBSESolutions.com)place digit is 4
Therefore, ³√91125 = 45

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