### 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

**Ques. **Find the volume of a cube, one face of which has an area of 25 m^{2}.

(a) 145 m^{3}

(b) 175 m^{3}

(c) 225 m^{3}

(d) 125 m^{3}

Ans. (d)

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**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 m^{3}. 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)

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**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)

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**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)