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## Wednesday, 24 February 2021

### CBSE Class 8 Maths - MCQ and Online Tests - Unit 7 - Cubes and Cube Roots

#### CBSE Class 8 Maths – MCQ and Online Tests –  Unit 7 – Cubes and Cube Roots

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#### CBSE Class 8 Maths – MCQ and Online Tests – Unit 7 – Cubes and Cube Roots

Question 1.
What is the one’s digit in the cube root of the cube number 5832 ?
(a) 2
(b) 4
(c) 6
(d) 8.

Hint:
8 × 8 × 8 = 512.

Question 2.
Find the smallest number by which the number 121 must be multiplied to obtain a perfect cube.
(a) 7
(b) 9
(c) 11
(d) 5.

Hint:
121 = 11 × 11.

Question 3.
Find the smallest number by which the number 88 must be divided to obtain a perfect cube.
(a) 11
(b) 5
(c) 7
(d) 9.

Hint:
88 = 2 × 2 × 2 × 11 = 2³ × 11.

Question 4.
What is the one’s digit in the cube root of the cube number 6859 ?
(a) 7
(b) 8
(c) 9
(d) 6.

Hint:
9 × 9 × 9 = 729.

Question 5.
Which of the following numbers is not a cube number ?
(a) 10000
(b) 3125
(c) 64
(d) 729.

Hint:
10000 = 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5.
= 24 × 54 = 2³ × 2 × 5³ × 5.

Question 6.
The cube of an odd natural number is
(a) even
(b) odd
(c) may be even, may be odd
(d) prime number.

Hint:
3 × 3 × 3 = 27 (odd).

Question 7.
The cube of an even natural number is
(a) even
(b) odd
(c) may be even, may be odd
(d) prime number.

Hint:
6 × 6 × 6 = 216 (even).

Question 8.
The one’s digit of the cube of the number 111 is
(a) 1
(b) 2
(c) 3
(d) 9.

Hint:
1 × 1 × 1 = 1.

Question 9.
The one’s digit of the cube of the number 242 is
(a) 2
(b) 4
(c) 6
(d) 8.

Hint:
2 × 2 × 2 = 8.

Question 10.
The one’s digit of the cube of the number 123 is
(a) 3
(b) 6
(c) 9
(d) 7.

Hint:
3 × 3 × 3 = 27.

Question 11.
The one’s digit of the cube of the number 144 is
(a) 1
(b) 2
(c) 3
(d) 4.

Hint:
4 × 4 × 4 = 64.

Question 12.
The one’s digit of the cube of the number 50 is
(a) 1
(b) 0
(c) 5
(d) 4.

Hint:
0 × 0 × 0 = 0.

Question 13.
The one’s digit of the cube of the number 326 is
(a) 2
(b) 3
(c) 6
(d) 4.

Hint:
6 × 6 × 6 = 216.

Question 14.
The one’s digit of the cube of the number 325 is
(a) 2
(b) 5
(c) 3
(d) 6.

Hint:
5 × 5 × 5 = 125.

Question 15.
The one’s digit of the cube of the number 347 is
(a) 3
(b) 4
(c) 7
(d) 1.

Hint:
7 × 7 × 7 = 343.

Question 16.
The one’s digit of the cube of the number 68 is
(a) 1
(b) 2
(c) 6
(d) 8.

Hint:
8 × 8 × 8 = 512.

Question 17.
The one’s digit of the cube of the number 249 is
(a) 2
(b) 4
(c) 9
(d) 1.

Hint:
9 × 9 × 9 = 729.

Question 18.
What is the one’s digit in the cube root of the cube number 1331 ?
(a) 1
(b) 2
(c) 3
(d) 4

Hint:
1 × 1 × 1 = 1.

Question 19.
What is the one’s digit in the cube root of the cube number 1000000 ?
(a) 0
(b) 1
(c) 2
(d) 9.

Hint:
0 × 0 × 0 = 0.

Question 20.
What is the one’s digit in the cube root of the cube number 3375 ?
(a) 2
(b) 3
(c) 5
(d) 4.

Hint:
5 × 5 × 5 = 125.

Question 21.
What is the one’s digit in the cube root of the cube number 4096 ?
(a) 2
(b) 6
(c) 4
(d) 9.

Hint:
6 × 6 × 6 = 216.

Question 22.
What is the one’s digit in the cube root of the cube number 4913 ?
(a) 7
(b) 9
(c) 3
(d) 6.

Hint:
7 × 7 × 7 = 343.

Question 23.
Which of the following numbers is a perfect cube ?
(a) 125
(b) 36
(c) 75
(d) 100.

Hint:
125 = 5 × 5 × 5 = 5³.

Question 24.
Which of the following numbers is a cube number ?
(a) 1000
(b) 400
(c) 100
(d) 600.

Hint:
1000 = 10 × 10 × 10 = 10³.

Question 25.
Which of the following numbers is not a perfect cube ?
(a) 1331
(b) 512
(c) 343
(d) 100.

Hint:
100 = 2 × 2 × 5 × 5 = 2² × 5².

Question 26.
The volume of a cube is 64 cm³. The edge of the cube is
(a) 4 cm
(b) 8 cm
(c) 16 cm
(d) 6 cm.

Hint:
Edge = $$\sqrt[3]{64}$$ = $$\sqrt[3]{2 × 2 × 2 × 2 × 2 × 2}$$
= $$\sqrt[3]{2^3×2^3}$$ = 2 × 2 = 4.

Question 27.
Apala makes a cuboid of plasticine of sides 5 cm, 4 cm, 2 cm. How many such cuboids will be needed to form a cube ?
(a) 20
(b) 25
(c) 10
(d) 16.

Hint:
Volume = 5 × 4 × 2 = 5 × 2 × 2 × 2
= 5 × 2³.

Question 28.
Which of the following is false ?
(a) Cube of any odd number is odd
(b) A perfect cube does not end with two zeroes
(c) The cube of a single digit number may be a single digit number
(d) There is no perfect cube which ends with 8.

Hint:
1728 = 12³.

Question 29.
What is the one’s digit in the cube root of the cube number 8000 ?
(a) 0
(b) 2
(c) 4
(d) 8.

Hint:
0 × 0 × 0 = 0.

Question 30.
The number of zeroes at the end of the cube of the number 20 is
(a) 1
(b) 2
(c) 3
(d) 6.

Hint:
? Number of zeroes at the end of the number 20 = 1
? Number of zeroes at the end of its cube = 3 × 1 = 3.

Question 31.
The number of zeroes at the end of the cube root of the cube number 1000 is
(a) 1
(b) 2
(c) 3
(d) 4.

Hint:
? Number of zeroes at the end of the cube = 3
? Number of zeroes at the end of the cube root = $$\frac{3}{3}$$ = 1.

Question 32.
The number of zeroes at the end of the cube of the number 100 is
(a) 1
(b) 2
(c) 4
(d) 6.

Hint:
? Number of zeroes at the end of the number 100 = 2
? Number of zeroes at the end of its cube = 3 × 2 = 6.

Question 33.
The number of zeroes at the end of the cube root of the cube number 8000000 is
(a) 1
(b) 2
(c) 3
(d) 6.

Hint:
? Number of zeroes at the end of the cube = 6
? Number of zeroes at the end of the cube root = $$\frac{6}{3}$$ = 2.

Question 34.
Find the smallest number by which the number 108 must be multiplied to obtain a perfect cube.
(a) 2
(b) 3
(c) 4
(d) 5.

Hint:
108 = 2 × 2 × 3 × 3 × 3 = 2 × 2 × 3³.

Question 35.
Find the smallest number by which the number 250 must be divided to obtain a perfect cube.
(o) 2
(b) 3
(c) 4
(d) 5.

Hint:
250 = 5 × 5 × 5 × 2 = 5³ × 2.

Question 36.
Find the smallest number by which the number 72 must be multiplied to obtain a perfect cube.
(a) 2
(b) 3
(c) 4
(d) 6.

Hint:
72 = 2 × 2 × 2 × 3 × 3 = 2³ × 3 × 3.

Question 37.
Find the smallest number by which the number 375 must be divided to obtain a perfect cube.
(a) 2
(b) 3
(c) 5
(d) 4.

Hint:
375 = 3 × 5 × 5 × 5 = 3 × 5³.

Question 38.
Find the smallest number by which the number 100 must be multiplied to obtain a perfect cube.
(a) 5
(b) 2
(c) 4
(d) 10.

Hint:
100 = 2 × 2 × 5 × 5.

Question 39.
Find the smallest number by which the number 10000 must be divided to obtain a perfect cube.
(a) 2
(b) 5
(c) 10
(d) 100

Hint:
10000 = 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5
= 2³ × 2 × 5³ × 5.

Question 40.
Find the smallest number by which the number 200 must be multiplied to obtain a perfect cube.
(a) 2
(b) 10
(c) 5
(d) 100.

Hint:
200 = 2 × 2 × 2 × 5 × 5 = 2³ × 5 × 5.

Question 41.
Find the smallest number by which the number 625 must be divided to obtain a perfect cube.
(a) 3
(b) 5
(c) 25
(d) 125.

Hint:
625 = 5 × 5 × 5 × 5 = 5³ × 5.

Question 42.
Find the smallest number by which the number 128 must be multiplied to obtain a perfect cube.
(a) 2
(b)4
(c) 3
(d) 8.

Hint:
128 = 2 × 2 × 2 × 2 × 2 × 2 × 2
= 2³ × 2³ × 2.

Question 43.
Find the smallest number by which the number 256 must be divided to obtain a perfect cube.
(a) 2
(b) 4
(c) 8
(d) 16.

Hint:
256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
= 2³ × 2³ × 2 × 2.

Question 44.
Find the smallest number by which the number 36 must be multiphed to obtain a perfect cube.
(a) 6
(b) 2
(c) 3
(d) 4.

Hint:
36 = 2 × 2 × 3 × 3.

Question 45.
Find the smallest number by which the number 1296 must be divided to obtain a perfect cube.
(a) 6
(b) 2
(c) 4
(d) 3.

Hint:
1296 =2 × 2 × 2 × 2 × 3 × 3 × 3 × 3
= 2³ × 2 × 3³ × 3.

Question 46.
Find the smallest number by which the number 392 must be multiplied to obtain a perfect cube.
(a) 3
(b) 5
(c) 7
(d) 6.

Hint:
392 = 2 × 2 × 2 × 7 × 7 = 2³ × 7 × 7.

Question 47.
Find the smallest number by which the number 2401 must be divided to obtain a perfect cube.
(a) 7
(b) 6
(c) 5
(d) 9.

Hint:
2401 = 7 × 7 × 7 × 7 = 7³ × 7.

Question 48.
What is the one’s digit in the cube root of the cube number 1728 ?
(a) 1
(b) 2
(c) 3
(d) 9.

Hint:
2 × 2 × 2 = 8.

Question 49.
What is the one’s digit in the cube root of the cube number 2197 ?
(a) 1
(b) 2
(c) 3
(d) 7.

Hint:
3 × 3 × 3 = 27.

Question 50.
What is the one’s digit in the cube root of the cube number 2744 ?
(a) 1
(b) 2
(c) 3
(d) 4.