Rs Aggarwal 2018 Solutions for Class 8 Math Chapter 4 Cubes And Cube Roots are provided here with simple step-by-step explanations. These solutions for Cubes And Cube Roots are extremely popular among Class 8 students for Math Cubes And Cube Roots Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rs Aggarwal 2018 Book of Class 8 Math Chapter 4 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rs Aggarwal 2018 Solutions. All Rs Aggarwal 2018 Solutions for class Class 8 Math are prepared by experts and are 100% accurate.
Page No 64:
Question 1:
Evaluate:
(i) (8)3
(ii) (15)3
(iii) (21)3
(iv) (60)3
Answer:
(i) (8)3 = = 512.
Thus, the cube of 8 is 512.
(ii) (15)3 = = 3375.
Thus, the cube of 15 is 3375.
(iii) (21)3 = = 9261.
Thus, the cube of 21 is 9261.
(iv) (60)3 = = 216000.
Thus, the cube of 60 is 216000.
Page No 64:
Question 2:
Evaluate:
(i) (1.2)3
(ii) (3.5)3
(iii) (0.8)3
(iv) (0.05)3
Answer:
(i) (1.2)3 = = 1.728
Thus, the cube of 1.2 is 1.728.
(ii) (3.5)3= = 42.875
Thus, the cube of 3.5 is 42.875.
(iii) (0.8)3= = 0.512
Thus, the cube of 0.8 is 0.512.
(iv) (0.05)3= = 0.000125
Thus, the cube of 0.05 is 0.000125.
Page No 65:
Question 3:
Evaluate:
(i)
(ii)
(iii)
(iv)
Answer:
(i)
Thus, the cube of is
(ii)
Thus, the cube of is
(iii)
Thus, the cube of is
(iv)
Thus, the cube of is .
Page No 65:
Question 4:
Which of the following numbers are perfect cubes? In case of perfect cube, find the number whose cube is the given number.
(i) 125
(ii) 243
(iii) 343
(iv) 256
(v) 8000
(vi) 9261
(vii) 5324
(viii) 3375
Answer:
(i) 125
Resolving 125 into prime factors:
125 = 555
Here, one triplet is formed, which is . Hence, 125 can be expressed as the product of the triplets of 5.
Therefore, 125 is a perfect cube.
(ii) 243 is not a perfect cube.
(iii) 343
Resolving 125 into prime factors:
343 = 777
Here, one triplet is formed, which is . Hence, 343 can be expressed as the product of the triplets of 7.
Therefore, 343 is a perfect cube.
(iv) 256 is not a perfect cube.
(v) 8000
Resolving 8000 into prime factors:
8000 = 222222555
Here, three triplets are formed, which are 23, 23 and 53. Hence, 8000 can be expressed as the product of the triplets of 2, 2 and 5, i.e. = .
Therefore, 8000 is a perfect cube.
(vi) 9261
Resolving 9261 into prime factors:
9261 = 333777
Here, two triplets are formed, which are and . Hence, 9261 can be expressed as the product of the triplets of 3 and 7, i.e. = .
Therefore, 9261 is a perfect cube.
(vii) 5324 is not a perfect cube.
(viii) 3375 .
Resolving 3375 into prime factors:
3375 = 333555.
Here, two triplets are formed, which are and . Hence, 3375 can be expressed as the product of the triplets of 3 and 5, i.e. = .
Therefore, 3375 is a perfect cube.
Page No 65:
Question 5:
Which of the following are the cubes of even numbers?
(i) 216
(ii) 729
(iii) 512
(iv) 3375
(v) 1000
Answer:
The cubes of even numbers are always even. Therefore, 216, 512 and 1000 are the cubes of even numbers.
216 = 222333 =
512 =
1000 =
Page No 65:
Question 6:
Which of the following are the cubes of odd numbers?
(i) 125
(ii) 343
(iii) 1728
(iv) 4096
(v) 9261
Answer:
The cube of an odd number is an odd number. Therefore, 125, 343 and 9261 are the cubes of odd numbers.
125 = 555 =
343 = 777 =
9261 = 333777 = =
Page No 65:
Question 7:
Find the smallest number by which 1323 must be multiplied so that the product is a perfect cube.
Answer:
1323
1323 = .
To make it a perfect cube, it has to be multiplied by 7.
Page No 65:
Question 8:
Find the smallest number by which 2560 must be multiplied so that the product is a perfect cube.
Answer:
2560
2560 can be expressed as the product of prime factors in the following manner:
2560 =
To make this a perfect square, we have to multiply it by 55.
Therefore, 2560 should be multiplied by 25 so that the product is a perfect cube.
Page No 65:
Question 9:
What is the smallest number by which 1600 must be divided so that the quotient is a perfect cube?
Answer:
1600
1600 can be expressed as the product of prime factors in the following manner:
1600 =
Therefore, to make the quotient a perfect cube, we have to divide 1600 by:
Page No 65:
Question 10:
Find the smallest number by which 8788 must be divided so that the quotient is a perfect cube.
Answer:
8788
8788 can be expressed as the product of prime factors as .
Therefore, 8788 should be divided by 4, i.e. (), so that the quotient is a perfect cube.
Page No 66:
Question 1:
Find the value of using the short-cut method:
(25)3
Answer:
Here, a = 2 and b = 5
Using the formula :
4 2 |
4 15 |
25 6 |
25 5 |
8 7 |
60 16 |
150 12 |
125 |
15 | 76 | 162 |
∴ = 15625
Page No 66:
Question 2:
Find the value of using the short-cut method:
(47)3
Answer:
Here, a = 4 and b = 7
Using the formula :
16 4 |
16 21 |
49 12 |
49 7 |
64 39 |
336 62 |
588 34 |
343 |
103 | 398 | 622 |
∴ = 103823
Page No 66:
Question 3:
Find the value of using the short-cut method:
(68)3
Answer:
Here, a = 6 and b = 8
Using the formula :
36 6 |
36 24 |
64 18 |
64 8 |
216 98 |
864 120 |
1152 51 |
512 |
314 | 984 | 1203 |
∴ = 314432
Page No 66:
Question 4:
Find the value of using the short-cut method:
(84)3
Answer:
Here, a = 8 and b = 4
Using the formula :
64 8 |
64 12 |
16 24 |
16 4 |
512 80 |
768 39 |
384 6 |
64 |
592 | 807 | 390 |
∴ = 592704
Page No 67:
Question 1:
Evaluate:
Answer:
By prime factorisation:
64 =
=
∴
Page No 67:
Question 2:
Evaluate:
Answer:
By prime factorisation:
343 =
= ( )
∴
Page No 67:
Question 3:
Evaluate:
Answer:
By prime factorisation:
729 =
=
∴ =
Page No 67:
Question 4:
Evaluate:
Answer:
By prime factorisation:
1728 =
=
∴ =
Page No 67:
Question 5:
Evaluate:
Answer:
By prime factorisation:
9261 =
=
∴ =
Page No 67:
Question 6:
Evaluate:
Answer:
By prime factorisation:
4096 =
=
∴ =
Page No 67:
Question 7:
Evaluate:
Answer:
By prime factorisation:
8000 =
=
∴ =
Page No 67:
Question 8:
Evaluate:
Answer:
By prime factorisation:
3375 =
=
∴ =
Page No 68:
Question 9:
Evaluate:
Answer:
By prime factorisation:
216 =
=
=
∴ =
Page No 68:
Question 10:
Evaluate:
Answer:
By prime factorisation:
=
=
=
∴ =
Page No 68:
Question 11:
Evaluate:
Answer:
By prime factorisation:
=
=
∴
Page No 68:
Question 12:
Evaluate:
Answer:
By prime factorisation:
= = =
∴ =
Page No 68:
Question 13:
Evaluate:
Answer:
By prime factorisation:
= =
∴ =
Page No 68:
Question 14:
Evaluate:
Answer:
By factorisation:
=
∴ =
Page No 68:
Question 15:
Evaluate:
Answer:
On factorisation:
=
∴ =
Page No 68:
Question 16:
Evaluate:
Answer:
=
=
=
= = 36
Page No 68:
Question 17:
Evaluate:
Answer:
On factorisation:
= =
=
Page No 68:
Question 18:
Evaluate:
Answer:
By factorisation:
=
=
Page No 68:
Question 1:
Tick (✓) the correct answer
Which of the following numbers is a perfect cube?
(a) 141
(b) 294
(c) 216
(d) 496
Answer:
(a)
141 is not a perfect cube.
(b)
294 is not a perfect cube.
(c) (✓)
216 is a perfect cube.
216 =
(d)
496 is not a perfect cube.
Page No 68:
Question 2:
Tick (✓) the correct answer
Which of the following numbers is a perfect cube?
(a) 1152
(b) 1331
(c) 2016
(d) 739
Answer:
(a)
1152 = .
Hence, 1152 is not a perfect cube.
(b) (✓)
1331 =
Hence, 1331 is a perfect cube.
(c)
2016 =
Hence, 2016 is not a perfect cube.
(d)
739 is not a perfect cube.
Page No 68:
Question 3:
Tick (✓) the correct answer
(a) 6
(b) 7
(c) 8
(d) 9
Answer:
(c) 8
=
=
Hence, the cube root of 512 is 8.
Page No 68:
Question 4:
Tick (✓) the correct answer
(a) 100
(b) 40
(c) 20
(d) 30
Answer:
(c) 20
Hence, the cube root of is 20.
Page No 68:
Question 5:
Tick (✓) the correct answer
(a)
(b)
(c)
(d)
Answer:
(b)
=
=
∴ =
Page No 68:
Question 6:
Tick (✓) the correct answer
(a)
(b)
(c)
(d)
Answer:
(b)
=
=
∴ =
Page No 68:
Question 7:
Tick (✓) the correct answer
By what least number should 648 be multiplied to get a perfect cube?
(a) 3
(b) 6
(c) 9
(d) 8
Answer:
(c) 9
648 =
Therefore, to get a perfect cube, we need to multiply 648 by 9, i.e. .
Page No 68:
Question 8:
Tick (✓) the correct answer
By what least number should 1536 be divided to get a perfect cube?
(a) 3
(b) 4
(c) 6
(d) 8
Answer:
(a) 3
1536 =
Therefore, to get a perfect cube, we need to divide 1536 by 3.
Page No 68:
Question 9:
Tick (✓) the correct answer
(a)
(b)
(c)
(d) none of these
Answer:
(c)
∴ =
Page No 68:
Question 10:
Tick (✓) the correct answer
(0.8)3 = ?
(a) 51.2
(b) 5.12
(c) 0.512
(d) none of these
Answer:
(c) 0.512
∴ =
Page No 70:
Question 1:
Evaluate
Answer:
=
∴ =
Page No 70:
Question 2:
Evaluate
Answer:
By prime factorisation method:
=
= .
∴ =
Page No 70:
Question 3:
Evaluate
Answer:
By prime factorisation:
=
=
∴ =
Page No 70:
Question 4:
Evaluate
Answer:
By prime factorisation method:
=
=
∴ =
Page No 70:
Question 5:
Mark (✓) against the correct answer
(a)
(b)
(c)
(d) none of these
Answer:
(c)
=
= =
∴ =
Page No 70:
Question 6:
Mark (✓) against the correct answer
Which of the following numbers is a perfect cube?
(a) 121
(b) 169
(c) 196
(d) 216
Answer:
(d) 216
216 =
216 = 63
Hence, 216 is a perfect cube.
Page No 70:
Question 7:
Mark (✓) against the correct answer
(a) 64
(b) 32
(c) 24
(d) 36
Answer:
(c) 24
=
=
=
∴ = 24
Page No 70:
Question 8:
Mark (✓) against the correct answer
(a)
(b)
(c)
(d)
Answer:
(b)
By prime factorisation:
=
= =
∴ =
Page No 70:
Question 9:
Mark (✓) against the correct answer
By what least number should 324 be multiplied to get a perfect cube?
(a) 12
(b) 14
(c) 16
(d) 18
Answer:
(d) 18
324 =
Therefore, to show that the given number is the product of three triplets, we need to multiply 324 by .
In other words, we need to multiply 324 by 18 to make it a perfect cube.
Page No 70:
Question 10:
Mark (✓) against the correct answer
(a)
(b)
(c)
(d) none of these
Answer:
(b)
Resolving the numerator and the denominator into prime factors:
Page No 70:
Question 11:
Mark (✓) against the correct answer
Which of the following is a cube of an odd number?
(a) 216
(b) 512
(c) 343
(d) 1000
Answer:
(c) 343
The cube of an odd number will always be an odd number.
Therefore, 343 is the cube of an odd number.
Page No 70:
Question 12:
Fill in the blanks.
(i)
(ii)
(iii)
(iv) (0.5)3 = .........
Answer:
(i)
(ii)
(iii)
(iv) 0.125
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