A Square and A Cube Class 8 MCQ Maths Chapter 1

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MCQ on A Square and A Cube Class 8

A Square and A Cube MCQ Class 8

Class 8 Maths MCQ Chapter 1 A Square and A Cube

Multiple Choice Questions

Question 1.
The total non-square numbers between the squares of 30 and 31 are
(a) 60
(b) 61
(c) 62
(d) 63
Answer:
(a) 60

Question 2.
If a number has 2 or 2 at its unit’s place, then its square would end in
(a) 2
(b) 8
(c) 4
(d) 16
Answer:
(c) 4

Question 3.
How many perfect square numbers lie between 16 and 81?
(a) 4
(b) 5
(c) 6
(d) 8
Answer:
(a) 4

Question 4.
The maximum number of digits in the cube root of a six-digit number is
(a) 1
(b) 2
(c) 3
(d) 6
Answer:
(b) 2

Question 5.
Cube root of 8 is
(a) 512
(b) 64
(c) 2
(d) 4
Answer:
(c) 2

Question 6.
Which of the following numbers can not be a perfect square?
(a) 2500
(b) 1600
(c) 961
(d) 468
Answer:
(d) 468

Question 7.
Which of the following numbers would not have the digit 4 at its unit place?
(a) 52²
(b) 68²
(c) 34²
(d) 102²
Answer:
(c) 34²

Question 8.
The cube of a number
(a) is always positive
(b) is always negative
(c) may be positive or negative
(d) can never be zero
Answer:
(c) may be positive or negative

Question 9.
If a number ends in 3, then its cube ends in
(a) 3
(b) 9
(c) 7
(d) 7 or 9
Answer:
(c) 7

Question 10.
If a number ends in 7, then its cube ends in
(a) 7
(b) 8
(c) 7 and 9
(d) 3
Answer:
(d) 3

Question 11.
The partner factors of 25 is/are
(a) 1, 25
(b) 5, 5
(c) 2, 25
(d) Both (a) and (b)
Answer:
(d) Both (a) and (b)

Question 12.
Which of the following cannot be a perfect square?
(a) 841
(b) 529
(c) 198
(d) All of these
Answer:
(c) 198

Question 13.
A number ending in 9 will have the unit place of its square as
(a) 1
(b) 3
(c) 9
(d) 6
Answer:
(a) 1

Question 14.
Which of the following is not a unit digit of a square number?
(a) 0
(b) 4
(c) 6
(d) 8
Answer:
(d) 8

Question 15.
A perfect square number having m digits, where m is even will have square root with
(a) \(\frac{m}{2}\) digits
(b) \(\frac{m+1}{2}\) digits
(c) m + 1 digits
(d) \(\frac{m}{3}\) digits
Answer:
(a) \(\frac{m}{2}\) digits

Question 16.
Which of the following is a square of an even number?
(a) 144
(b) 169
(c) 441
(d) 625
Answer:
(a) 144

Question 17.
How many numbers lie between the squares of 13 and 14?
(a) 28
(b) 26
(c) 13
(d) 14
Answer:
(b) 26

Question 18.
If 45² = 2025 then 46² is equal to
(a) 2025 + 46
(b) 2025 + 46²
(c) 2025 + 23²
(d) 2025 + 91
Answer:
(d) 2025 + 91

Question 19.
The value of 1 + 3 + 5 + 7 + 9 + 11 + 13 is
(a) 36
(b) 41
(c) 49
(d) 52
Answer:
(c) 49

Question 20.
The value of 198² – 197² is
(a) 393
(b) 395
(c) 295
(d) 293
Answer:
(b) 395

Question 21.
The square root of 196 is
(a) 12
(b) 11
(c) 15
(d) 14
Answer:
(d) 14

Question 22.
The smallest square number that is divisible by each of the numbers 2, 3 and 8 is
(a) 64
(b) 144
(c) 1296
(d) 576
Answer:
(b) 144

Question 23.
The cube of 24 is
(a) 12167
(b) 15625
(c) 13824
(d) 10648
Answer:
(c) 13824

Question 24.
Which of the following number is a perfect cube?
(a) 243
(b) 512
(c) 392
(d) 8640
Answer:
(b) 512

Question 25.
Which of the following numbers is not a perfect cube?
(a) 216
(b) 343
(c) 125
(d) 667
Answer:
(d) 667

Question 26.
Which of the following is the cube of an even natural number?
(a) 1331
(b) 4913
(c) 3375
(d) 1728
Answer:
(d) 1728

Question 27.
The ones digit of the cube of 23 is
(a) 3
(b) 6
(c) 7
(d) 9
Answer:
(c) 7

Question 28.
The value of 21 + 23 + 25 + 27 + 29 is equal to
(a) 33
(b) 63
(c) 43
(d) 53
Answer:
(d) 53

Question 29.
The value of 23³ – 22³ is
(a) 1518
(b) 1519
(c) 1421
(d) 1420
Answer:
(b) 1519

Question 30.
The smallest number by which 841 be multiplied so that the product becomes a perfect cube is
(a) 29
(b) 27
(c) 25
(d) 23
Answer:
(a) 29

Question 31.
The cube root of 6859 is
(a) 19
(b) 18
(c) 17
(d) 21
Answer:
(a) 19

Question 32.
What is the value of \(\frac{\sqrt[3]{64}+\sqrt[3]{125}}{\sqrt[3]{27}}\) ?
(a) 2
(b) 3
(c) 4
(d) 9
Answer:
(b) 3

Assertion-Reason Type Questions

Question 1.
Assertion (A) The square root of a perfect square is always a whole number.
Reason (R) A perfect square is a number that can be expressed as the product of an integer by itself.
(e.g. 9 = 3 × 3 or 16 = 4 × 4)
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Answer:
(a) Both A and R are true and R is the correct explanation of A.

Question 2.
Assertion (A) 6838 is a perfect square number.
Reason (R) A perfect square number can never have 8 at unit place.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Answer:
(d) A is false but R is true.

Question 3.
Assertion (A) The cube of an even number is always an even number.
Reason (R) When you multiply an even number by itself three times, the result is always even.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Answer:
(a) Both A and R are true and R is the correct explanation of A.

Question 4.
Assertion (A) Finding the cube root of a number is the inverse operation of finding the cube of that number. Reason (R) If you take the cube root of a number and then cube, the result you will get back to the original number.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Answer:
(a) Both A and R are true and R is the correct explanation of A.

Fill in the blanks

1. The square of an even number is _______ and square of an odd number is _______
Answer:
even, odd

2. If a number ends in 2, 3, 7 or 8 it can never be a _______
Answer:
perfect square

3. The square of multiple of 10 always ends in _______ number of zeros.
Answer:
even

4. If a number has digits 3 or 7 in its unit’s place, then its square ends in _______
Answer:
9

5. Finding square root is the inverse operation of _______ and finding cube root is the inverse operation of _______
Answer:
squaring; cubing

6. Cube root of a negative number is _______
Answer:
negative

7. If a number ends in 8, its cube ends in _______
Answer:
8

8. The pair/pairs of partner factors of 5 is/are _________
Answer:
(1, 5)

9. The unit digit in the square of 1456 is _________
Answer:
6

10. The 26th odd number is _________
Answer:
51

11. The square root of 24025 will have _________ digits.
Answer:
3

12. The least number by which 125 be multiplied to make it a perfect square is _________
Answer:
5

13. The cube of 12.5 is _________
Answer:
1953.125

14. Cube of a number ending in 7 will end in the digit _________
Answer:
3

15. The cube of 90 will have _________ zeroes.
Answer:
3

16. The value of 7³ – 6³ is _________
Answer:
127

17. The least number by which 72 is divided to make it a perfect cube is _________.
Answer:
9

State true-false

Question 1.
The square of an odd number can not be even.
Answer:
True

Question 2.
If a number ends in 0, 1, 4, 5, 6 or 9, then it must be a perfect square.
Answer:
False

Question 3.
If a number ends in 4, its square ends in 4.
Answer:
False

Question 4.
The product of two square numbers is also a square number.
Answer:
True

Question 5.
A number ending in an even number of zeros is always a perfect square.
Answer:
False

Question 6.
If a square ends with 5, then its cube ends with 25.
Answer:
False

Question 7.
A perfect cube does not end with 2 zeros.
Answer:
True

Question 8.
The cube of a single-digit number may be a single-digit number.
Answer:
True

Question 9.
Cube root of a negative integer is positive.
Answer:
False

Question 10.
The square of 2.3 is 5.29.
Answer:
True

Question 11.
The square of 87 will have 3 at the unit place.
Answer:
False

Question 12.
The number of zeroes at the end of a perfect square is always even.
Answer:
True

Question 13.
The sum of first 36 odd natural number is 1260.
Answer:
False

Question 14.
The cube of 1.5 is 3.325.
Answer:
False

Question 15.
999 is a perfect cube.
Answer:
False

Question 16.
Cube roots of 8 are +2 and -2.
Answer:
False

Match the following

Question 1.

Column A	Column B
(i) Number of zeros in (400)2	(a) 1
(ii) Non-perfect squares between 52 and 62	(b) 8
(iii) Square root of 121	(c) 10
(iv) Unit digit of 472	(d) 11
(v) Unit digit of \(\sqrt[3]{54872}\)	(e) 4
(vi) Cube root of the smallest natural number	(f) 9

Answer:

Column A	Column B
(i) Number of zeros in (400)2	(e) 4
(ii) Non-perfect squares between 52 and 62	(c) 10
(iii) Square root of 121	(d) 11
(iv) Unit digit of 472	(f) 9
(v) Unit digit of \(\sqrt[3]{54872}\)	(b) 8
(vi) Cube root of the smallest natural number	(a) 1

Question 2.
Match the Column I with Column II.

Column 1 (Number)	Column II (Square root)
(a) 441	(i) 14
(b) 289	(ii) 9
(c) 81	(iii) 17
(d) 196	(iv) 21

Answer:

Column 1 (Number)	Column II (Square root)
(a) 441	(iv) 21
(b) 289	(iii) 17
(c) 81	(ii) 9
(d) 196	(i) 14

Question 3.
Match the Column I with Column II.

Column I	Column II
(a) Cube of 26 is	(i) 17576
(b) Cube root of 21952	(ii) 144
(c) \(\sqrt[3]{125}+(\sqrt[2]{625})^3\)	(iii) 28
(d) \((\sqrt[2]{25})^3+\sqrt[3]{6859}\)	(iv) 15630

Answer:

Column I	Column II
(a) Cube of 26 is	(i) 17576
(b) Cube root of 21952	(iii) 28
(c) \(\sqrt[3]{125}+(\sqrt[2]{625})^3\)	(iv) 15630
(d) \((\sqrt[2]{25})^3+\sqrt[3]{6859}\)	(ii) 144

Subjective Questions

Question 1.
Express 196 as the sum of 14 odd numbers.
Answer:
1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 + 27

Question 2.
Without adding, find the sum:
(i) 1 + 3 + 5 + 7 + 9 + 11
(ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17
Answer:
(i) 6² = 36
(ii) 9² = 81

Question 3.
What will be the number of zeros in the squares of the following numbers:
(i) 400
(ii) 30
Answer:
(i) 4
(ii) 2

Question 4.
How many natural numbers lie between
(i) 91² and 20²?
(ii) 92² and 20²?
Answer:
(i) 38
(ii) 182

Question 5.
Express the following as the sum of two consecutive integers:
(i) 17²
(ii) 23²
Answer:
(i) 8 + 9
(ii) 11 + 12

Question 6.
Rohini makes a cuboid of sides 7 cm, 3 cm, and 7 cm. How many such cuboids will she need to form a cube?
Answer:
63

Question 7.
Find the smallest number by which 1458 must be multiplied to obtain a perfect square. Also, find the square root of the perfect square so obtained.
Answer:
2; 54

Question 8.
Find the smallest whole number by which 1620 must be divided to obtain a perfect square. Also, find the square root of the perfect square so obtained.
Answer:
5; 18

Question 9.
5625 persons are sitting in a theatre in such a manner that there are as many persons in a row as there are rows in the theatre. How many rows are there in a theatre?
Answer:
75

Question 10.
The area of a square plot is 2304 m². Find the length of a side of the square plot.
Answer:
48 m

Question 11.
Is 100 a perfect cube? If not, then find the smallest number by which it is multiplied to get a perfect cube.
Answer:
No; 10

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