RBSE Solutions for Class 8 Maths Chapter 2 Cube and Cube Roots Additional Questions 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 Additional Questions.
| Board | RBSE |
| Textbook | SIERT, Rajasthan |
| Class | Class 8 |
| Subject | Maths |
| Chapter | Chapter 2 |
| Chapter Name | Cube and Cube Roots |
| Exercise | Additional Questions |
| Number of Questions | 31 |
| Category | RBSE Solutions |
Rajasthan Board RBSE Class 8 Maths Chapter 2 Cube and Cube Roots Additional Questions
I. Objective Type Questions
Question 1.
How many consecutive odd numbers will be required to get 10³?
(a) 5
(b) 8
(c) 10
(d) 100
Question 2.
How many perfect cube numbers are there in between 1 to 1000?
(a) 10
(b) 18
(c) 25
(d) 52
Question 3.
The cube of 7 is
(a) 49
(b) 243
(c) 343
(d) 21
Question 4.
What is the cube root of 13824?
(a) 24
(b) 56
(c) 18
(d) 124
Question 5.
The least natural number by 392 should be multiplied to get a number which is a perfect cube is
(a) 2
(b) 3
(c) 5
(d) 7
Question 6.
Cube root – 216 is
(a) 6
(b) 16
(c) – 6
(d) – 16
Question 7.
Cube of 80 is
(a) 51200
(b) 512000
(c) 512
(d) 520
Question 8.
The cube root of \(\frac { 343 }{ 512 }\) is
(a) \(\frac { 7 }{ 18 }\)
(b) \(\frac { 7 }{ 8 }\)
(c) \(\frac { -7 }{ 8 }\)
(d) \(\frac { -7 }{ 18 }\)
Question 9.
The cube-root of 1000 is
(a) 1
(b) 10
(c) 100
(d) 1000
Answers
1. (c)
2. (a)
3. (c)
4. (a)
5. (d)
6. (c)
7. (b)
8. (b)
9. (b).
II. Fill in the blanks
Question 1.
Cubes of even numbers are ____
Question 2.
The unit’s digit of the cube of 18 is ___
Question 3.
The operation(RBSESolutions.com)of finding the ___ is the opposite operation of finding the cube.
Question 4.
The cube root is denoted by the___sign.
Question 5.
The cube root of 8,57,375 is ___
Ans.
1. even,
2. 2,
3. cube root,
4. ³√
5. 95
III. True/False Type Questions
State true or false.
(i) Cube of any odd number is even.
(ii) A perfect cube(RBSESolutions.com)does not end with two zeros.
(iii) If square of a number ends with 5, then its cube ends with 25.
(iv) There is no perfect cube which ends with 8.
(v) The cube of a two digit(RBSESolutions.com)number may be a three digit number.
(vi) The cube of a two digit number may have seven or more digits.
(vii) The cube of a single digit number may be a single digit number.
Solution
(i) False
(ii) True
(iii) False
(iv) False
(v) False
(vi) False
(vii) True
IV. Very Short Answer Type Questions
Question 1.
What do you mean by Hardi- Ramanujan number?
Solution.
The number expressible as the sum of two cubes in two different ways, are called Hardi-Ramanujan numbers. For eg. 1729, 4104, 13832 etc.
Question 2.
What do you mean by the cube of a number?
Solution.
The number obtained after multiplying a number thrice by itself is called cube of that number.
Question 3.
Express 9³ as the sum of consecutive odd numbers?
Solution.
73 + 75 + 77 + 79 + 81 + 83 + 85 + 87 + 89 = 729 = 9³
Question 4.
Find the cube root(RBSESolutions.com)of 8000 by prime factorization method.
Solution.
8000 = 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5
∴ ³√8000 = 2 x 2 x 5 = 20.
Question 5.
Find the least number by which 1188 should be divided so as to get a perfect cube number.
Solution.
Prime factors of 1188
= 2 x 2 x 3 x 3 x 3 x 11
Remaining factors after obtaining the triples, are 2 x 2 x 11. So we need to divide 1188 by 2 x 2 x 11 = 44 to get a perfect cube.
Question 6.
Find cube root of 9261 by prime factor method.
Solution.
Resolving 9261 into prime factors as follows :
V. Short Answer Type Questions
Question 1.
Suman makes a cuboid of soil of sides 15 cm, 30 cm and 15 cm. How many such cuboids will he need to form a cube?
Solution.
Volume of a cuboid
= 15 x 30 x 15
=3 x 5 x 2 x 3 x 5 x 3 x 5
= 2 x 3 x 3 x 3 x 5 x 5 x 5
In above. By Prime factorization 2 comes only one time there fore such, cuboid will he need to form a cube = 2 x 2 = 4 Ans.
Question 2.
Mansi has a cuboidal box whose sides are 5 cm, 3 cm and 5 cm. How many such cuboidal boxes will be required for making one cubical box?
Solution.
Volume of cuboidal box
= 5 x 3 x 5
= 5 x 5 x 3
To make it a cube, we require 5 x 3 x 3 = 45
i. e., 45 such cuboids Ans.
Question 3.
State true or false : for any integer m, m2 < m3. Why?
Solution.
We take m = 2, 3, 4 etc.
We see that
When m – 2 :
m2 = 22 = 2 x 2 = 4 and m3 = 23 = 2 x 2 x 2 = 8 Clearly, 4 < 8, i.e. m2 < m3
When m = 3 :
m2 = 32 = 3 x 3 = 9 and m3 = 33 = 3 x 3 x 3 = 27 Clearly, 9 < 27, i.e. m2 < m3
When m = 4 :
m2 = 42 = 4 x 4 = 16 and m3 = 43 = 4 x 4 x 4 = 64 Clearly, 16 < 64, i.e. m2 < m3
But when m = 1,
m2 = 12 = 1 x 1 = 1 and m3 = 13 = 1 x 1 x 1 = 1
Then m2 < m3
Thus we can say that for any positive integer (natural number) m > 1, m2 < m3 is true.
Now, consider m = – 1, – 2, – 3 etc.
When m = – 1 :
m2 = (- 1)2 = (- 1) x (- 1) = 1
and m3 = (- 1)3 = (- 1) x (- 1) x (- 1) = – 1
Clearly, 1 > – 1, i.e. m2 > m3
When m = — 2 :
m2 = (- 2)2 = (- 2) x (- 2) = 4 and
m3 = (- 2)3 = (- 2) x (- 2) x (- 2) = – 8
Clearly, 4 > – 8, i.e. m2 > m3
Thus we can say that for any negative
integer m, m2 < m3 is false.
Question 4.
Ratio of three number are 2:3:4 and sum of their cubes is 33957. Find the greatest number.
Solution.
Let three(RBSESolutions.com)number are 2x, 3x and 4x
According to question,
(2x)3 + (3x)3 + (4x)3 = 33957
⇒ 8x3 + 27x3 + 64x3 = 33957
⇒ 99x3 = 33957
⇒ x3 = \(\frac { 33957 }{ 99 }\)
⇒ x3 = 343
⇒ x3 = 7 x 7 x 7 = (7)3
⇒ x= 3√(7)3 = 7
Therefore, the greatest number = 4x = 4 x 7 = 28 Ans.
Question 5.
Volume of a cube is 9261000 m3. Find the side of cube.
Solution.
Let side of a cube = a m
then volume of a cube = a x a x a = a3
According(RBSESolutions.com)to question, a3 = 9261000
a = 3√9261000
a = \(\sqrt [ 3 ]{ \underline { 2\times 2\times 2 } \times \underline { 3\times 3\times 3 } \times \underline { 5\times 5\times 5 } \times \underline { 7\times 7\times 7 } } \)
a = 2 x 3 x 5 x 7 = 210 m
∴ side of a cube = 210 m. Ans.
We hope the given RBSE Solutions for Class 8 Maths Chapter 2 Cube and Cube Roots Additional Questions will help you. If you have any query regarding Rajasthan Board RBSE Class 8 Maths Chapter 2 Cube and Cube Roots Additional Questions, drop a comment below and we will get back to you at the earliest.