# Cube Root Problems ### Cubes and Cube Root practice worksheet:

Ques. Which of the following are cubes of even natural numbers?
(a) 512
(b) 3375
(c) 1728
(d) 1728
Ans. (a)

Ques. What is the smallest number by which 675 may be divided so that the quotient is a perfect cube?
(a) 25
(b) 15
(c) 35
(d) 17
Ans. (a)

Ques. By what least number 4320 be multiplied to obtain a number which is a perfect cube?
(a) 25
(b) 40
(c) 60
(d) 50

Ans. (d)

Ques. Find the volume of a cube, one face of which has an area of 25 m2.
(a) 145 m3
(b) 175 m3
(c) 225 m3
(d) 125 m3
Ans. (d)

Ques. Find the cube root of 33698267
(a) 26
(b) 420
(c) 54
(d) 323
Ans. (d)

Ques. The cube root of 1331 is :
(a) 11
(b) 13
(c) 19
(d) 17
Ans. (a)

Ques. Three numbers are in the ratio 2 : 3 : 4. Sum of their cubes is 33957, then the numbers are
(a) 14, 21, 28
(b) 15, 22, 29
(c) 13, 20, 27
(d) none of these
Ans. (a)

Ques. Find the cube root of 729 by prime factorization method:
(a) 17
(b) 7
(c) 13
(d) 9
Ans. (d)

Ques. The volume of a cubical box is 474.552 cubic metres. Find the length of each side of the box.
(a) 8.8 m
(b) 7.8 m
(c) 7.3 m
(d) 7.2 m
Ans. (b)

Ques. The volume of a cube is 9261000 m3. Find the side of the cube.
(a) 230 m
(b) 220 m
(c) 210 m
(d) 240 m
Ans. (c)

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Ques. By which smallest number must 35721 be divided so that the quotient is perfect cube?
(a) 1600
(b) 1728
(c) 49
(d) 6859
Ans. (c)

Ques. What is the smallest number by which 35721 must be multiplied, so that the products are perfect cubes?
(a) 7
(b) 5
(c) 49
(d) 27
Ans. (c)

Ques. Cube root of 17064 is
(a) 24.746
(b) 25.746
(c) 26.746
(d) 27.746
Ans. (b)

Ques. Find the cube root of each of 140 x 2450:
(a) 70
(b) 60
(c) 50
(d) 40
Ans. (a)

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Ques. Which of the following are cubes of odd natural numbers?
(a) 1728
(b) 4096
(c) 1000
(d) 343
Ans. (d)

Ques. Cube root of 175616 is
(a) 65
(b) 56
(c) 76
(d) none of these
Ans. (b)

Ques. Find the cube of 0.2.
(a) 0.006
(b) 0.012
(c) 0.008
(d) 0.08
Ans. (c)

Ques. Show that –216 / 42875 is the cube of a rational number. Also, find that rational number.
(a) –9 /25
(b) –7 /45
(c) –4 /35
(d) –6 /35
Ans. (d)

Ques. Find the cube root of 0.003375
(a) 0.12
(b) 0.13
(c) 0.15
(d) 0.18
Ans. (c)

Ques. Which of the following are cubes of even natural numbers?
(a) 13824
(b) 3375
(c) 456533
(d) 1728
Ans. (a)

Ques. Find the smallest number(s) by which 3087 must be multiplied so that the product has a perfect cube root.
(a) 3
(b) 6
(c) 7
(d) 9
Ans. (a)

Ques. Find the units digit of the cube root of 571787
(a) 7
(b) 6
(c) 5
(d) 4
Ans. (a)

Ques. Which of the following number are not perfect cubes?
(a) 216
(b) 128
(c) 46656
(d) 1000
Ans. (b)

Ques. One’s digit of the cube of 5022 will be
(a) 2
(b) 4
(c) 8
(d) none of these
Ans. (c)

Ques. By which smallest number must the 1600 be divided so that the quotient is perfect cube?
(a) 7
(b) 17
(c) 4
(d) 25
Ans. (d)

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Ques. Is 27/125 a cube of rational number?
(a) 3/7
(b) 3/5
(c) 3/5
(d) 9/25
Ans. (b)

Ques. Volume of a cubical box is 32.768 cubic metres. Length of one side of cube is
(a) 2.3 m
(b) 3.2 m
(c) 4.2 m
(d) 5.2 m
Ans. (b)

Ques. Find the cube root of 1000000:
(a) 100
(b) 1000
(c) 10000
(d) None of these
Ans. (a)

Ques. Find the cube root 1.331
(a) 1.1
(b) 1.3
(c) 1.5
(d) 1.7
Ans. (a)

Ques. What is the smallest number by which 2560 must be multiplied, so that the products are perfect cubes?
(a) 343
(b) 25
(c) 17
(d) 27
Ans. (b)

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Ques. Find the cube root of each of –2300 x 5290
(a) –60
(b) –230
(c) –23
(d) –58
Ans. (b)

Ques. Write the units digit of the cube of 109:
(a) 7
(b) 9
(c) 3
(d) 5
Ans. (b)

Ques. Find the cube root of 405224
(a) 56
(b) 62
(c) 78
(d) 74
Ans. (d)

Ques. Smallest number by which 8640 be divided that quotient is a perfect cube will be
(a) 5
(b) 10
(c) 15
(d) 20
Ans. (a)

Ques. Find the cube root of 10648 / 12167
(a) 12 / 13
(b) 22 / 23
(c) 32 / 33
(d) 42 / 43
Ans. (b)

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Ques. By which smallest number must 107811 be divided so that the quotient is perfect cube?
(a) 3
(b) 25
(c) 1728
(d) 4096
Ans. (a)

Ques. Which of the following are cubes of odd natural numbers?
(a) 6859
(b) 4096
(c) 2095
(d) 512
Ans. (a)

Ques. Which of the following numbers are perfect cubes?
(a) 256
(b) 432
(c) 1728
(d) 15625
Ans. (d)

Ques. Find the cube root of “–571787”
(a) –83
(b) –53
(c) –27
(d) –76
Ans. (a)

Ques. What is the smallest number by which 8192 must be divided so that quotient is a perfect cube?
(a) 16
(b) 20
(c) 2
(d) 10
Ans. (c)

Ques. What is the smallest number by which 7803 must be multiplied, so that the products are perfect cubes?
(a) 17
(b) 125
(c) 25
(d) 109
Ans. (a)

Ques. Find the cube root of 13824.
(a) 24
(b) 26
(c) 28
(d) 32
Ans. (a)

Ques. Find the cube root of 9261000 by prime factorization method:
(a) 220
(b) 210
(c) 230
(d) 190
Ans. (b)

Ques. Find the cube root of “– 5832”
(a) –18
(b) 18
(c) 28
(d) -14
Ans. (a)

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Ques. Write the units digit of the cube of 833
(a) 7
(b) 9
(c) 4
(d) 2
Ans. (a)

Ques. Find the cube root of 438976 by prime factorization method:
(a) 76
(b) 78
(c) 62
(d) 66
Ans. (a)

Ques. By which smallest number must 8788 be divided so that the quotient is perfect cube?
(a) 4
(b) 25
(c) 6
(d) 343
Ans. (a)

Ques. Find the smallest number which when multiplied by 3600 will make the product a perfect cube.
(a) 40
(b) 80
(c) 60
(d) 30
Ans. (c)

Ques. Find the cube roots of 91125:
(a) 911
(b) 9
(c) 73
(d) 27
Ans. (c)

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Ques. Find the smallest number which when multiplied with 3600 will make the product a perfect cube.
(a) 27
(b) 60
(c) 90
(d) 33
Ans. (b)

Ques. What is the smallest number by which 106480 may be multiplied so that the product is a perfect cube?
(a) 70
(b) 80
(c) 100
(d) 110
Ans. (c)

Ques. Find the cube root of 2744000
(a) 120
(b) 140
(c) 160
(d) 10
Ans. (b)

Ques. Find the cube root of 250047 by prime factorization method:
(a) 65
(b) 63
(c) 61
(d) 59
Ans. (b)

Ques. What is that number whose cube is 3375?
(a) 7
(b) 25
(c) 35
(d) 15
Ans. (d)