NCERT Solutions for Class 8 Maths Chapter 7 Cubes and Cube Roots Ex 7.2 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 7 Cubes and Cube Roots Ex 7.2.
| Board | CBSE |
| Textbook | NCERT |
| Class | Class 8 |
| Subject | Maths |
| Chapter | Chapter 7 |
| Chapter Name | Cubes and Cube Roots |
| Exercise | Ex 7.2 |
| Number of Questions Solved | 3 |
| Category | NCERT Solutions |
NCERT Solutions for Class 8 Maths Chapter 7 Cubes and Cube Roots Ex 7.2
Ex 7.2 Class 8 Maths Question 1.
Find the cube root of each of the following numbers by prime factorisation method :
(i) 64
(ii) 512
(iii) 10648
(iv) 27000
(v) 15625
(vi) 13824
(vii) 110592
(viii) 46656
(ix) 175616
(x) 91125
Solution:
(i) Resolving 64 into prime factors, we get
64 = 2 x 2 x 2 x 2 x 2 x 2
∴
(ii) Resolving 512 into prime factors, we get
512 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
∴
![\sqrt [ 3 ]{ 64 } =\left( 2\times 2 \right) =4](http://s0.wp.com/latex.php?latex=%5Csqrt+%5B+3+%5D%7B+64+%7D+%3D%5Cleft%28+2%5Ctimes+2+%5Cright%29+%3D4&bg=ffffff&fg=000&s=0 "\sqrt [ 3 ]{ 64 } =\left( 2\times 2 \right) =4")
![\sqrt [ 3 ]{ 512 } =\left( 2\times 2\times 2 \right) =8](http://s0.wp.com/latex.php?latex=%5Csqrt+%5B+3+%5D%7B+512+%7D+%3D%5Cleft%28+2%5Ctimes+2%5Ctimes+2+%5Cright%29+%3D8&bg=ffffff&fg=000&s=0 "\sqrt [ 3 ]{ 512 } =\left( 2\times 2\times 2 \right) =8")
(iii) Resolving 10648 into prime factors, we get
10648 = 2 x 2 x 2 x 11 x 11 x 11
∴
![\sqrt [ 3 ]{ 10648 } =\left( 2\times 11 \right) =22](http://s0.wp.com/latex.php?latex=%5Csqrt+%5B+3+%5D%7B+10648+%7D+%3D%5Cleft%28+2%5Ctimes+11+%5Cright%29+%3D22&bg=ffffff&fg=000&s=0 "\sqrt [ 3 ]{ 10648 } =\left( 2\times 11 \right) =22")
(iv) Resolving 27000 into prime factors, we get
27000 = 1000 x 27
= 10 x 10 x 10 x 3 x 3 x 3 = 2 x 5 x 2 x 5 x 2 x 5 x 3 x 3 x 3
= 2 x 2 x 2 x 3 x 3 x 3 x 5 x 5 x 5
∴
![\sqrt [ 3 ]{ 27000 } =2\times 3\times 5=30](http://s0.wp.com/latex.php?latex=%5Csqrt+%5B+3+%5D%7B+27000+%7D+%3D2%5Ctimes+3%5Ctimes+5%3D30&bg=ffffff&fg=000&s=0 "\sqrt [ 3 ]{ 27000 } =2\times 3\times 5=30")
(v) Resolving 15625 into prime factors, we get
15625 = 5 x 5 x 5 x 5 x 5 x5
∴
![\sqrt [ 3 ]{ 15625 } =5\times 5=25](http://s0.wp.com/latex.php?latex=%5Csqrt+%5B+3+%5D%7B+15625+%7D+%3D5%5Ctimes+5%3D25&bg=ffffff&fg=000&s=0 "\sqrt [ 3 ]{ 15625 } =5\times 5=25")
(vi) Resolving 13824 into prime factors, we get
13824 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3
∴
![\sqrt [ 3 ]{ 13824 } =\left( 2\times 2\times 2\times 3 \right) =24](http://s0.wp.com/latex.php?latex=%5Csqrt+%5B+3+%5D%7B+13824+%7D+%3D%5Cleft%28+2%5Ctimes+2%5Ctimes+2%5Ctimes+3+%5Cright%29+%3D24&bg=ffffff&fg=000&s=0 "\sqrt [ 3 ]{ 13824 } =\left( 2\times 2\times 2\times 3 \right) =24")
(vii) Resolving 110592 in prime factors, we get
110592 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3
∴
![\sqrt [ 3 ]{ 110592 } =\left( 2\times 2\times 2\times 2\times 3 \right) =48](http://s0.wp.com/latex.php?latex=%5Csqrt+%5B+3+%5D%7B+110592+%7D+%3D%5Cleft%28+2%5Ctimes+2%5Ctimes+2%5Ctimes+2%5Ctimes+3+%5Cright%29+%3D48&bg=ffffff&fg=000&s=0 "\sqrt [ 3 ]{ 110592 } =\left( 2\times 2\times 2\times 2\times 3 \right) =48")
(viii) Resolving 46656 in prime factors, we get
46656 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3
∴
![\sqrt [ 3 ]{ 46656 } =\left( 2\times 2\times 3\times 3 \right) =36](http://s0.wp.com/latex.php?latex=%5Csqrt+%5B+3+%5D%7B+46656+%7D+%3D%5Cleft%28+2%5Ctimes+2%5Ctimes+3%5Ctimes+3+%5Cright%29+%3D36&bg=ffffff&fg=000&s=0 "\sqrt [ 3 ]{ 46656 } =\left( 2\times 2\times 3\times 3 \right) =36")
(ix) Resolving 175616 in prime factors, we get
175616 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 7 x 7 x 7 = (2 x 2 x 2 x 7)
= 56
(x) Resolving 91125 in prime factors, we get
91125 = 3 x 3 x 3 x 3 x 3 x 3 x 5 x 5 x 5
∴
![\sqrt [ 3 ]{ 91125 } =\left( 3\times 3\times 5 \right) =45](http://s0.wp.com/latex.php?latex=%5Csqrt+%5B+3+%5D%7B+91125+%7D+%3D%5Cleft%28+3%5Ctimes+3%5Ctimes+5+%5Cright%29+%3D45&bg=ffffff&fg=000&s=0 "\sqrt [ 3 ]{ 91125 } =\left( 3\times 3\times 5 \right) =45")
Ex 7.2 Class 8 Maths Question 2.
State true or false :
(i) Cube of any odd number is even.
(ii) A perfect cube 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 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, as 152 = 225 and 153 = 3375
(iv) False, as 8 = 23, 1728 =123, etc.
(v) False
(vi) False, as 103 = 1000, 993 = 970299
(vii) True, as 13 = 1, 23 =8.
Ex 7.2 Class 8 Maths Question 3.
You are told that 1,331 is a perfect cube. Can you guess without factorisation what is its cube root? Similarly, guess the cube roots of 4913, 12167, 32768.
Solution:
For 1331 :
Units digit of the cube root of 1331 is 1 as unit’s digit of the cube root of numbers ending in 1 is 1 . After striking three digits from the right of 1331, we get the number 1. Since 13 = 1, so the ten’s digit of the cube root of given number is 1.
∴
![\sqrt [ 3 ]{ 1331 } =11](http://s0.wp.com/latex.php?latex=%5Csqrt+%5B+3+%5D%7B+1331+%7D+%3D11&bg=ffffff&fg=000&s=0 "\sqrt [ 3 ]{ 1331 } =11")
For 4913 :
Units digit of the cube root of 4913 is 7 as unit’s digit of cube root of numbers ending in 3 is 7. After striking three digits from the right of 4913, we get the number 4. As 13 =1 and 23 =8, so 13 < 4 < 23. Therefore, the ten’s digit of cube root of 4913 is 1.
∴
![\sqrt [ 3 ]{ 4913 } =17](http://s0.wp.com/latex.php?latex=%5Csqrt+%5B+3+%5D%7B+4913+%7D+%3D17&bg=ffffff&fg=000&s=0 "\sqrt [ 3 ]{ 4913 } =17")
For 12167 :
Unit’s digit of the cube root of 12167 is 3 as unit’s digit of cube root of numbers ending in 7 is 3. After striking three digits from the right of 12167, we get the number 12. As 23 =8 and 33 =27, so 23 < 12 < 33. So, the ten’s digit of the cube root of 12167 is 2.
∴
![\sqrt [ 3 ]{ 12167 } =23](http://s0.wp.com/latex.php?latex=%5Csqrt+%5B+3+%5D%7B+12167+%7D+%3D23&bg=ffffff&fg=000&s=0 "\sqrt [ 3 ]{ 12167 } =23")
For 32768 :
Unit’s digit of the cube root of 32768 is 2 as unit’s digit of cube root of numbers ending in 8 is 2. After striking three digits from the right of 32768, we get the number 32. As 33 =27 and 43 = 64, so 33 < 32< 43. So, the ten’s digit of the cube root of 32768 is 3.
∴
![\sqrt [ 3 ]{ 32768 } =32](http://s0.wp.com/latex.php?latex=%5Csqrt+%5B+3+%5D%7B+32768+%7D+%3D32&bg=ffffff&fg=000&s=0 "\sqrt [ 3 ]{ 32768 } =32")
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