Class 8 Exam > Class 8 Notes > Mathematics (Maths) Class 8 > RD Sharma Solutions: Exercise 4.5 - Cubes & Cube Roots
Exercise 4.5 - Cubes & Cube Roots RD Sharma Solutions | Mathematics (Maths) Class 8 PDF Download
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Page 1
Question:54
Making use of the cube root table, find the cube roots 7
Solution:
Because 7 lies between 1 and 100, we will look at the row containing 7 in the column of x.
By the cube root table, we have:
3
v 7 = 1. 913
Thus, the answer is 1.913.
Question:55
Making use of the cube root table, find the cube root
70
Solution:
Because 70 lies between 1 and 100, we will look at the row containing 70 in the column of x.
By the cube root table, we have:
3
v 70 = 4. 121
Question:56
Making use of the cube root table, find the cube root
700
Solution:
We have:
700 = 70 ×10
? Cube root of 700 will be in the column of
3
v 10x against 70.
By the cube root table, we have:
3
v 700 = 8. 879
Thus, the answer is 8.879.
Question:57
Making use of the cube root table, find the cube root
7000
Solution:
We have:
7000 = 70 ×100
?
3
v 7000 =
3
v 7 ×1000 =
3
v 7 ×
3
v 1000
By the cube root table, we have:
3
v 7 = 1. 913 and
3
v 1000 = 10
?
3
v 7000 =
3
v 7 ×
3
v 1000 = 1. 913 ×10 = 19. 13
Question:58
Making use of the cube root table, find the cube root
1100
Solution:
We have:
1100 = 11 ×100
?
3
v 1100 =
3
v 11 ×100 =
3
v 11 ×
3
v 100
By the cube root table, we have:
3
v 11 = 2. 224 and
3
v 100 = 4. 642
?
3
v 1100 =
3
v 11 ×
3
v 100 = 2. 224 ×4. 642 = 10. 323 Up to three decimal places
Thus, the answer is 10.323.
Question:59
Making use of the cube root table, find the cube root
780
Solution:
We have:
( )
Page 2
Question:54
Making use of the cube root table, find the cube roots 7
Solution:
Because 7 lies between 1 and 100, we will look at the row containing 7 in the column of x.
By the cube root table, we have:
3
v 7 = 1. 913
Thus, the answer is 1.913.
Question:55
Making use of the cube root table, find the cube root
70
Solution:
Because 70 lies between 1 and 100, we will look at the row containing 70 in the column of x.
By the cube root table, we have:
3
v 70 = 4. 121
Question:56
Making use of the cube root table, find the cube root
700
Solution:
We have:
700 = 70 ×10
? Cube root of 700 will be in the column of
3
v 10x against 70.
By the cube root table, we have:
3
v 700 = 8. 879
Thus, the answer is 8.879.
Question:57
Making use of the cube root table, find the cube root
7000
Solution:
We have:
7000 = 70 ×100
?
3
v 7000 =
3
v 7 ×1000 =
3
v 7 ×
3
v 1000
By the cube root table, we have:
3
v 7 = 1. 913 and
3
v 1000 = 10
?
3
v 7000 =
3
v 7 ×
3
v 1000 = 1. 913 ×10 = 19. 13
Question:58
Making use of the cube root table, find the cube root
1100
Solution:
We have:
1100 = 11 ×100
?
3
v 1100 =
3
v 11 ×100 =
3
v 11 ×
3
v 100
By the cube root table, we have:
3
v 11 = 2. 224 and
3
v 100 = 4. 642
?
3
v 1100 =
3
v 11 ×
3
v 100 = 2. 224 ×4. 642 = 10. 323 Up to three decimal places
Thus, the answer is 10.323.
Question:59
Making use of the cube root table, find the cube root
780
Solution:
We have:
( )
780 = 78 ×10
? Cube root of 780 would be in the column of
3
v 10x against 78.
By the cube root table, we have:
3
v 780 = 9. 205
Thus, the answer is 9.205.
Question:60
Making use of the cube root table, find the cube root
7800
Solution:
We have:
7800 = 78 ×100
?
3
v 7800 =
3
v 78 ×100 =
3
v 78 ×
3
v 100
By the cube root table, we have:
3
v 78 = 4. 273 and
3
v 100 = 4. 642
3
v 7800 =
3
v 78 ×
3
v 100 = 4. 273 ×4. 642 = 19. 835 upto three decimal places
Thus, the answer is 19.835
Question:61
Making use of the cube root table, find the cube root
1346
Solution:
By prime factorisation, we have:
1346 = 2 ×673 ?
3
v 1346 =
3
v 2 ×
3
v 673
Also
670 < 673 < 680 ?
3
v 670 <
3
v 673 <
3
v 680
From the cube root table, we have:
3
v 670 = 8. 750 and
3
v 680 = 8. 794
For the difference (680 -670), i.e., 10, the difference in the values
= 8. 794 -8. 750 = 0. 044
? For the difference of (673 -670), i.e., 3, the difference in the values
=
0.044
10
×3 = 0. 0132 = 0. 013 uptothreedecimalplaces
?
3
v 673 = 8. 750 +0. 013 = 8. 763
Now
3
v 1346 =
3
v 2 ×
3
v 673 = 1. 260 ×8. 763 = 11. 041 uptothreedecimalplaces
Thus, the answer is 11.041.
Question:62
Making use of the cube root table, find the cube root
250
Solution:
We have:
250 = 25 ×100
? Cube root of 250 would be in the column of
3
v 10x against 25.
By the cube root table, we have:
3
v 250 = 6. 3
Thus, the required cube root is 6.3.
Question:63
Making use of the cube root table, find the cube root
5112
Solution:
By prime factorisation, we have:
5112 = 2
3
×3
2
×71 ?
3
v 5112 = 2 ×
3
v 9 ×
3
v 71
( )
Page 3
Question:54
Making use of the cube root table, find the cube roots 7
Solution:
Because 7 lies between 1 and 100, we will look at the row containing 7 in the column of x.
By the cube root table, we have:
3
v 7 = 1. 913
Thus, the answer is 1.913.
Question:55
Making use of the cube root table, find the cube root
70
Solution:
Because 70 lies between 1 and 100, we will look at the row containing 70 in the column of x.
By the cube root table, we have:
3
v 70 = 4. 121
Question:56
Making use of the cube root table, find the cube root
700
Solution:
We have:
700 = 70 ×10
? Cube root of 700 will be in the column of
3
v 10x against 70.
By the cube root table, we have:
3
v 700 = 8. 879
Thus, the answer is 8.879.
Question:57
Making use of the cube root table, find the cube root
7000
Solution:
We have:
7000 = 70 ×100
?
3
v 7000 =
3
v 7 ×1000 =
3
v 7 ×
3
v 1000
By the cube root table, we have:
3
v 7 = 1. 913 and
3
v 1000 = 10
?
3
v 7000 =
3
v 7 ×
3
v 1000 = 1. 913 ×10 = 19. 13
Question:58
Making use of the cube root table, find the cube root
1100
Solution:
We have:
1100 = 11 ×100
?
3
v 1100 =
3
v 11 ×100 =
3
v 11 ×
3
v 100
By the cube root table, we have:
3
v 11 = 2. 224 and
3
v 100 = 4. 642
?
3
v 1100 =
3
v 11 ×
3
v 100 = 2. 224 ×4. 642 = 10. 323 Up to three decimal places
Thus, the answer is 10.323.
Question:59
Making use of the cube root table, find the cube root
780
Solution:
We have:
( )
780 = 78 ×10
? Cube root of 780 would be in the column of
3
v 10x against 78.
By the cube root table, we have:
3
v 780 = 9. 205
Thus, the answer is 9.205.
Question:60
Making use of the cube root table, find the cube root
7800
Solution:
We have:
7800 = 78 ×100
?
3
v 7800 =
3
v 78 ×100 =
3
v 78 ×
3
v 100
By the cube root table, we have:
3
v 78 = 4. 273 and
3
v 100 = 4. 642
3
v 7800 =
3
v 78 ×
3
v 100 = 4. 273 ×4. 642 = 19. 835 upto three decimal places
Thus, the answer is 19.835
Question:61
Making use of the cube root table, find the cube root
1346
Solution:
By prime factorisation, we have:
1346 = 2 ×673 ?
3
v 1346 =
3
v 2 ×
3
v 673
Also
670 < 673 < 680 ?
3
v 670 <
3
v 673 <
3
v 680
From the cube root table, we have:
3
v 670 = 8. 750 and
3
v 680 = 8. 794
For the difference (680 -670), i.e., 10, the difference in the values
= 8. 794 -8. 750 = 0. 044
? For the difference of (673 -670), i.e., 3, the difference in the values
=
0.044
10
×3 = 0. 0132 = 0. 013 uptothreedecimalplaces
?
3
v 673 = 8. 750 +0. 013 = 8. 763
Now
3
v 1346 =
3
v 2 ×
3
v 673 = 1. 260 ×8. 763 = 11. 041 uptothreedecimalplaces
Thus, the answer is 11.041.
Question:62
Making use of the cube root table, find the cube root
250
Solution:
We have:
250 = 25 ×100
? Cube root of 250 would be in the column of
3
v 10x against 25.
By the cube root table, we have:
3
v 250 = 6. 3
Thus, the required cube root is 6.3.
Question:63
Making use of the cube root table, find the cube root
5112
Solution:
By prime factorisation, we have:
5112 = 2
3
×3
2
×71 ?
3
v 5112 = 2 ×
3
v 9 ×
3
v 71
( )
By the cube root table, we have:
3
v 9 = 2. 080 and
3
v 71 = 4. 141
?
3
v 5112 = 2 ×
3
v 9 ×
3
v 71 = 2 ×2. 080 ×4. 141 = 17. 227 uptothreedecimalplaces
Thus, the required cube root is 17.227.
Question:64
Making use of the cube root table, find the cube root
9800
Solution:
We have:
9800 = 98 ×100
?
3
v 9800 =
3
v 98 ×100 =
3
v 98 ×
3
v 100
By cube root table, we have:
3
v 98 = 4. 610 and
3
v 100 = 4. 642
?
3
v 9800 =
3
v 98 ×
3
v 100 = 4. 610 ×4. 642 = 21. 40 uptothreedecimalplaces
Thus, the required cube root is 21.40.
Question:65
Making use of the cube root table, find the cube root
732
Solution:
We have:
730 < 732 < 740 ?
3
v 730 <
3
v 732 <
3
v 740
From cube root table, we have:
3
v 730 = 9. 004 and
3
v 740 = 9. 045
For the difference (740 -730), i.e., 10, the difference in values
= 9. 045 -9. 004 = 0. 041
? For the difference of (732 -730), i.e., 2, the difference in values
=
0.041
10
×2 = 0. 0082
?
3
v 732 = 9. 004 +0. 008 = 9. 012
Question:66
Making use of the cube root table, find the cube root
7342
Solution:
We have:
7300 < 7342 < 7400 ?
3
v 7000 <
3
v 7342 <
3
v 7400
From the cube root table, we have:
3
v 7300 = 19. 39 and
3
v 7400 = 19. 48
For the difference (7400 -7300), i.e., 100, the difference in values
= 19. 48 -19. 39 = 0. 09
? For the difference of (7342 -7300), i.e., 42, the difference in the values
=
0.09
100
×42 = 0. 0378 = 0. 037
?
3
v 7342 = 19. 39 +0. 037 = 19. 427
Question:67
Making use of the cube root table, find the cube root
133100
Solution:
We have:
133100 = 1331 ×100 ?
3
v 133100 =
3
v 1331 ×100 = 11 ×
3
v 100
By cube root table, we have:
3
v 100 = 4. 642
?
3
v 133100 = 11 ×
3
v 100 = 11 ×4. 642 = 51. 062
Page 4
Question:54
Making use of the cube root table, find the cube roots 7
Solution:
Because 7 lies between 1 and 100, we will look at the row containing 7 in the column of x.
By the cube root table, we have:
3
v 7 = 1. 913
Thus, the answer is 1.913.
Question:55
Making use of the cube root table, find the cube root
70
Solution:
Because 70 lies between 1 and 100, we will look at the row containing 70 in the column of x.
By the cube root table, we have:
3
v 70 = 4. 121
Question:56
Making use of the cube root table, find the cube root
700
Solution:
We have:
700 = 70 ×10
? Cube root of 700 will be in the column of
3
v 10x against 70.
By the cube root table, we have:
3
v 700 = 8. 879
Thus, the answer is 8.879.
Question:57
Making use of the cube root table, find the cube root
7000
Solution:
We have:
7000 = 70 ×100
?
3
v 7000 =
3
v 7 ×1000 =
3
v 7 ×
3
v 1000
By the cube root table, we have:
3
v 7 = 1. 913 and
3
v 1000 = 10
?
3
v 7000 =
3
v 7 ×
3
v 1000 = 1. 913 ×10 = 19. 13
Question:58
Making use of the cube root table, find the cube root
1100
Solution:
We have:
1100 = 11 ×100
?
3
v 1100 =
3
v 11 ×100 =
3
v 11 ×
3
v 100
By the cube root table, we have:
3
v 11 = 2. 224 and
3
v 100 = 4. 642
?
3
v 1100 =
3
v 11 ×
3
v 100 = 2. 224 ×4. 642 = 10. 323 Up to three decimal places
Thus, the answer is 10.323.
Question:59
Making use of the cube root table, find the cube root
780
Solution:
We have:
( )
780 = 78 ×10
? Cube root of 780 would be in the column of
3
v 10x against 78.
By the cube root table, we have:
3
v 780 = 9. 205
Thus, the answer is 9.205.
Question:60
Making use of the cube root table, find the cube root
7800
Solution:
We have:
7800 = 78 ×100
?
3
v 7800 =
3
v 78 ×100 =
3
v 78 ×
3
v 100
By the cube root table, we have:
3
v 78 = 4. 273 and
3
v 100 = 4. 642
3
v 7800 =
3
v 78 ×
3
v 100 = 4. 273 ×4. 642 = 19. 835 upto three decimal places
Thus, the answer is 19.835
Question:61
Making use of the cube root table, find the cube root
1346
Solution:
By prime factorisation, we have:
1346 = 2 ×673 ?
3
v 1346 =
3
v 2 ×
3
v 673
Also
670 < 673 < 680 ?
3
v 670 <
3
v 673 <
3
v 680
From the cube root table, we have:
3
v 670 = 8. 750 and
3
v 680 = 8. 794
For the difference (680 -670), i.e., 10, the difference in the values
= 8. 794 -8. 750 = 0. 044
? For the difference of (673 -670), i.e., 3, the difference in the values
=
0.044
10
×3 = 0. 0132 = 0. 013 uptothreedecimalplaces
?
3
v 673 = 8. 750 +0. 013 = 8. 763
Now
3
v 1346 =
3
v 2 ×
3
v 673 = 1. 260 ×8. 763 = 11. 041 uptothreedecimalplaces
Thus, the answer is 11.041.
Question:62
Making use of the cube root table, find the cube root
250
Solution:
We have:
250 = 25 ×100
? Cube root of 250 would be in the column of
3
v 10x against 25.
By the cube root table, we have:
3
v 250 = 6. 3
Thus, the required cube root is 6.3.
Question:63
Making use of the cube root table, find the cube root
5112
Solution:
By prime factorisation, we have:
5112 = 2
3
×3
2
×71 ?
3
v 5112 = 2 ×
3
v 9 ×
3
v 71
( )
By the cube root table, we have:
3
v 9 = 2. 080 and
3
v 71 = 4. 141
?
3
v 5112 = 2 ×
3
v 9 ×
3
v 71 = 2 ×2. 080 ×4. 141 = 17. 227 uptothreedecimalplaces
Thus, the required cube root is 17.227.
Question:64
Making use of the cube root table, find the cube root
9800
Solution:
We have:
9800 = 98 ×100
?
3
v 9800 =
3
v 98 ×100 =
3
v 98 ×
3
v 100
By cube root table, we have:
3
v 98 = 4. 610 and
3
v 100 = 4. 642
?
3
v 9800 =
3
v 98 ×
3
v 100 = 4. 610 ×4. 642 = 21. 40 uptothreedecimalplaces
Thus, the required cube root is 21.40.
Question:65
Making use of the cube root table, find the cube root
732
Solution:
We have:
730 < 732 < 740 ?
3
v 730 <
3
v 732 <
3
v 740
From cube root table, we have:
3
v 730 = 9. 004 and
3
v 740 = 9. 045
For the difference (740 -730), i.e., 10, the difference in values
= 9. 045 -9. 004 = 0. 041
? For the difference of (732 -730), i.e., 2, the difference in values
=
0.041
10
×2 = 0. 0082
?
3
v 732 = 9. 004 +0. 008 = 9. 012
Question:66
Making use of the cube root table, find the cube root
7342
Solution:
We have:
7300 < 7342 < 7400 ?
3
v 7000 <
3
v 7342 <
3
v 7400
From the cube root table, we have:
3
v 7300 = 19. 39 and
3
v 7400 = 19. 48
For the difference (7400 -7300), i.e., 100, the difference in values
= 19. 48 -19. 39 = 0. 09
? For the difference of (7342 -7300), i.e., 42, the difference in the values
=
0.09
100
×42 = 0. 0378 = 0. 037
?
3
v 7342 = 19. 39 +0. 037 = 19. 427
Question:67
Making use of the cube root table, find the cube root
133100
Solution:
We have:
133100 = 1331 ×100 ?
3
v 133100 =
3
v 1331 ×100 = 11 ×
3
v 100
By cube root table, we have:
3
v 100 = 4. 642
?
3
v 133100 = 11 ×
3
v 100 = 11 ×4. 642 = 51. 062
Question:68
Making use of the cube root table, find the cube root
37800
Solution:
We have:
37800 = 2
3
×3
3
×175 ?
3
v 37800 =
3
v
2
3
×3
3
×175 = 6 ×
3
v 175
Also
170 < 175 < 180 ?
3
v 170 <
3
v 175 <
3
v 180
From cube root table, we have:
3
v 170 = 5. 540 and
3
v 180 = 5. 646
For the difference (180 -170), i.e., 10, the difference in values
= 5. 646 -5. 540 = 0. 106
? For the difference of (175 -170), i.e., 5, the difference in values
=
0.106
10
×5 = 0. 053
?
3
v 175 = 5. 540 +0. 053 = 5. 593
Now
37800 = 6 ×
3
v 175 = 6 ×5. 593 = 33. 558
Thus, the required cube root is 33.558.
Question:69
Making use of the cube root table, find the cube root
0.27
Solution:
The number 0.27 can be written as
27
100
.
Now
3
v 0. 27 =
3 27
100
=
3
v
27
3
v
100
=
3
3
v
100
By cube root table, we have:
3
v 100 = 4. 642
?
3
v 0. 27 =
3
3
v
100
=
3
4.642
= 0. 646
Thus, the required cube root is 0.646.
Question:70
Making use of the cube root table, find the cube root
8.6
Solution:
The number 8.6 can be written as
86
10
.
Now
3
v 8. 6 =
3 86
10
=
3
v
86
3
v
10
By cube root table, we have:
3
v 86 = 4. 414 and
3
v 10 = 2. 154
?
3
v 8. 6 =
3
v
86
3
v
10
=
4.414
2.154
= 2. 049
Thus, the required cube root is 2.049.
Question:71
Making use of the cube root table, find the cube root
0.86
Solution:
The number 0.86 could be written as
86
100
.
Now
3
v 0. 86 =
3 86
100
=
3
v
86
3
v
100
v
v
v
Page 5
Question:54
Making use of the cube root table, find the cube roots 7
Solution:
Because 7 lies between 1 and 100, we will look at the row containing 7 in the column of x.
By the cube root table, we have:
3
v 7 = 1. 913
Thus, the answer is 1.913.
Question:55
Making use of the cube root table, find the cube root
70
Solution:
Because 70 lies between 1 and 100, we will look at the row containing 70 in the column of x.
By the cube root table, we have:
3
v 70 = 4. 121
Question:56
Making use of the cube root table, find the cube root
700
Solution:
We have:
700 = 70 ×10
? Cube root of 700 will be in the column of
3
v 10x against 70.
By the cube root table, we have:
3
v 700 = 8. 879
Thus, the answer is 8.879.
Question:57
Making use of the cube root table, find the cube root
7000
Solution:
We have:
7000 = 70 ×100
?
3
v 7000 =
3
v 7 ×1000 =
3
v 7 ×
3
v 1000
By the cube root table, we have:
3
v 7 = 1. 913 and
3
v 1000 = 10
?
3
v 7000 =
3
v 7 ×
3
v 1000 = 1. 913 ×10 = 19. 13
Question:58
Making use of the cube root table, find the cube root
1100
Solution:
We have:
1100 = 11 ×100
?
3
v 1100 =
3
v 11 ×100 =
3
v 11 ×
3
v 100
By the cube root table, we have:
3
v 11 = 2. 224 and
3
v 100 = 4. 642
?
3
v 1100 =
3
v 11 ×
3
v 100 = 2. 224 ×4. 642 = 10. 323 Up to three decimal places
Thus, the answer is 10.323.
Question:59
Making use of the cube root table, find the cube root
780
Solution:
We have:
( )
780 = 78 ×10
? Cube root of 780 would be in the column of
3
v 10x against 78.
By the cube root table, we have:
3
v 780 = 9. 205
Thus, the answer is 9.205.
Question:60
Making use of the cube root table, find the cube root
7800
Solution:
We have:
7800 = 78 ×100
?
3
v 7800 =
3
v 78 ×100 =
3
v 78 ×
3
v 100
By the cube root table, we have:
3
v 78 = 4. 273 and
3
v 100 = 4. 642
3
v 7800 =
3
v 78 ×
3
v 100 = 4. 273 ×4. 642 = 19. 835 upto three decimal places
Thus, the answer is 19.835
Question:61
Making use of the cube root table, find the cube root
1346
Solution:
By prime factorisation, we have:
1346 = 2 ×673 ?
3
v 1346 =
3
v 2 ×
3
v 673
Also
670 < 673 < 680 ?
3
v 670 <
3
v 673 <
3
v 680
From the cube root table, we have:
3
v 670 = 8. 750 and
3
v 680 = 8. 794
For the difference (680 -670), i.e., 10, the difference in the values
= 8. 794 -8. 750 = 0. 044
? For the difference of (673 -670), i.e., 3, the difference in the values
=
0.044
10
×3 = 0. 0132 = 0. 013 uptothreedecimalplaces
?
3
v 673 = 8. 750 +0. 013 = 8. 763
Now
3
v 1346 =
3
v 2 ×
3
v 673 = 1. 260 ×8. 763 = 11. 041 uptothreedecimalplaces
Thus, the answer is 11.041.
Question:62
Making use of the cube root table, find the cube root
250
Solution:
We have:
250 = 25 ×100
? Cube root of 250 would be in the column of
3
v 10x against 25.
By the cube root table, we have:
3
v 250 = 6. 3
Thus, the required cube root is 6.3.
Question:63
Making use of the cube root table, find the cube root
5112
Solution:
By prime factorisation, we have:
5112 = 2
3
×3
2
×71 ?
3
v 5112 = 2 ×
3
v 9 ×
3
v 71
( )
By the cube root table, we have:
3
v 9 = 2. 080 and
3
v 71 = 4. 141
?
3
v 5112 = 2 ×
3
v 9 ×
3
v 71 = 2 ×2. 080 ×4. 141 = 17. 227 uptothreedecimalplaces
Thus, the required cube root is 17.227.
Question:64
Making use of the cube root table, find the cube root
9800
Solution:
We have:
9800 = 98 ×100
?
3
v 9800 =
3
v 98 ×100 =
3
v 98 ×
3
v 100
By cube root table, we have:
3
v 98 = 4. 610 and
3
v 100 = 4. 642
?
3
v 9800 =
3
v 98 ×
3
v 100 = 4. 610 ×4. 642 = 21. 40 uptothreedecimalplaces
Thus, the required cube root is 21.40.
Question:65
Making use of the cube root table, find the cube root
732
Solution:
We have:
730 < 732 < 740 ?
3
v 730 <
3
v 732 <
3
v 740
From cube root table, we have:
3
v 730 = 9. 004 and
3
v 740 = 9. 045
For the difference (740 -730), i.e., 10, the difference in values
= 9. 045 -9. 004 = 0. 041
? For the difference of (732 -730), i.e., 2, the difference in values
=
0.041
10
×2 = 0. 0082
?
3
v 732 = 9. 004 +0. 008 = 9. 012
Question:66
Making use of the cube root table, find the cube root
7342
Solution:
We have:
7300 < 7342 < 7400 ?
3
v 7000 <
3
v 7342 <
3
v 7400
From the cube root table, we have:
3
v 7300 = 19. 39 and
3
v 7400 = 19. 48
For the difference (7400 -7300), i.e., 100, the difference in values
= 19. 48 -19. 39 = 0. 09
? For the difference of (7342 -7300), i.e., 42, the difference in the values
=
0.09
100
×42 = 0. 0378 = 0. 037
?
3
v 7342 = 19. 39 +0. 037 = 19. 427
Question:67
Making use of the cube root table, find the cube root
133100
Solution:
We have:
133100 = 1331 ×100 ?
3
v 133100 =
3
v 1331 ×100 = 11 ×
3
v 100
By cube root table, we have:
3
v 100 = 4. 642
?
3
v 133100 = 11 ×
3
v 100 = 11 ×4. 642 = 51. 062
Question:68
Making use of the cube root table, find the cube root
37800
Solution:
We have:
37800 = 2
3
×3
3
×175 ?
3
v 37800 =
3
v
2
3
×3
3
×175 = 6 ×
3
v 175
Also
170 < 175 < 180 ?
3
v 170 <
3
v 175 <
3
v 180
From cube root table, we have:
3
v 170 = 5. 540 and
3
v 180 = 5. 646
For the difference (180 -170), i.e., 10, the difference in values
= 5. 646 -5. 540 = 0. 106
? For the difference of (175 -170), i.e., 5, the difference in values
=
0.106
10
×5 = 0. 053
?
3
v 175 = 5. 540 +0. 053 = 5. 593
Now
37800 = 6 ×
3
v 175 = 6 ×5. 593 = 33. 558
Thus, the required cube root is 33.558.
Question:69
Making use of the cube root table, find the cube root
0.27
Solution:
The number 0.27 can be written as
27
100
.
Now
3
v 0. 27 =
3 27
100
=
3
v
27
3
v
100
=
3
3
v
100
By cube root table, we have:
3
v 100 = 4. 642
?
3
v 0. 27 =
3
3
v
100
=
3
4.642
= 0. 646
Thus, the required cube root is 0.646.
Question:70
Making use of the cube root table, find the cube root
8.6
Solution:
The number 8.6 can be written as
86
10
.
Now
3
v 8. 6 =
3 86
10
=
3
v
86
3
v
10
By cube root table, we have:
3
v 86 = 4. 414 and
3
v 10 = 2. 154
?
3
v 8. 6 =
3
v
86
3
v
10
=
4.414
2.154
= 2. 049
Thus, the required cube root is 2.049.
Question:71
Making use of the cube root table, find the cube root
0.86
Solution:
The number 0.86 could be written as
86
100
.
Now
3
v 0. 86 =
3 86
100
=
3
v
86
3
v
100
v
v
v
By cube root table, we have:
3
v 86 = 4. 414 and
3
v 100 = 4. 642
?
3
v 0. 86 =
3
v
86
3
v
100
=
4.414
4.642
= 0. 951 uptothreedecimalplaces
Thus, the required cube root is 0.951.
Question:72
Making use of the cube root table, find the cube root
8.65
Solution:
The number 8.65 could be written as
865
100
.
Now
3
v 8. 65 =
3 865
100
=
3
v
865
3
v
100
Also
860 < 865 < 870 ?
3
v 860 <
3
v 865 <
3
v 870
From the cube root table, we have:
3
v 860 = 9. 510 and
3
v 870 = 9. 546
For the difference (870 -860), i.e., 10, the difference in values
= 9. 546 -9. 510 = 0. 036
? For the difference of (865 -860), i.e., 5, the difference in values
=
0.036
10
×5 = 0. 018 uptothreedecimalplaces
?
3
v 865 = 9. 510 +0. 018 = 9. 528 uptothreedecimalplaces
From the cube root table, we also have:
3
v 100 = 4. 642
?
3
v 8. 65 =
3
v
865
3
v
100
=
9.528
4.642
= 2. 053 uptothreedecimalplaces
Thus, the required cube root is 2.053.
Question:73
Making use of the cube root table, find the cube root
7532
Solution:
We have:
7500 < 7532 < 7600 ?
3
v 7500 <
3
v 7532 <
3
v 7600
From the cube root table, we have:
3
v 7500 = 19. 57 and
3
v 7600 = 19. 66
For the difference (7600 -7500), i.e., 100, the difference in values
= 19. 66 -19. 57 = 0. 09
? For the difference of (7532 -7500), i.e., 32, the difference in values
=
0.09
100
×32 = 0. 0288 = 0. 029 uptothreedecimalplaces
?
3
v 7532 = 19. 57 +0. 029 = 19. 599
Question:74
Making use of the cube root table, find the cube root
833
Solution:
We have:
830 < 833 < 840 ?
3
v 830 <
3
v 833 <
3
v 840
From the cube root table, we have:
3
v 830 = 9. 398 and
3
v 840 = 9. 435
For the difference (840 -830), i.e., 10, the difference in values
= 9. 435 -9. 398 = 0. 037
v
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Document Description: RD Sharma Solutions: Exercise 4.5 - Cubes & Cube Roots for Class 8 2024 is part of Mathematics (Maths) Class 8 preparation.
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