Squares and Square Roots (MCQs)
MCQs Questions on Class 8 Chapter 6 Squares and Square Roots
Multiple Choice Questions (MCQs) are given for the Class 8 Chapter 6 Squares and Square Roots chapter. Each problem carries four options, in which one is the correct answer. Students have to find a solution for each problem and choose the correct answer.
Q. The perfect square number out of 2, 3, 4 and 5 is
(a) 2
(b) 3
(c) 4
(d) 5
Answer: (c). 4
Q. A perfect square number between 30 and 40 is
(a) 36
(b) 32
(c) 33
(d) 39
Answer: (a). 36
Q. Between 50 and 60, the perfect square number is
(a) 56
(b) 55
(c) 54
(d) none.
Answer: (d) none.
Q. Which of the following is a perfect square number ?
(a) 1067
(b) 7828
(c) 4333
(d) 625.
Answer: (d). 625
Hint:
Perfect square numbers end with
0, 1, 4, 5, 6 or 9 at unit’s place.
Q. Which of the following is a perfect square number ?
(a) 2222
(b) 32543
(c) 888
(d) 10000.
Answer: (d). 10000
Hint:
Perfect square numbers end with
0, 1, 4, 5, 6 or 9 at unit’s place
Q. Which of 132², 87², 72² and 209² would end with digit 1 ?
(a) 132²
(b) 87²
(c) 72²
(d) 209²
Answer: (d)209²
Hint:
If a number has 1 or 9 in the unit’s place, then its square ends in 1
Q. Which of 105², 216², 333² and 111² would end with digit 1 ?
(a) 105²
(b) 216²
(c) 333²
(d) 111².
Answer: (d) 111²
Hint:
If a number has 1 or 9 in the unit’s place, then its square ends in 1
Q. Which of 17², 34², 25² and 49²would have 6 at unit place ?
(a) 17²
(b) 34²
(c) 25²
(d) 49²
Answer: (b) 34²
Hint:
If a number has 4 or 6 in the unit’s place, then its square ends in 6.
Q. Which of 21², 33², 472 and 362 would have 6 at unit place ?
(a) 21²
(b) 33²
(c) 47²
(d) 36²
Answer: (d)36²
Hint:
If a number has 4 or 6 in the unit’s place, then its square ends in 6
Q. What will be the number of zeros in the square of the number 100 ?
(a) 2
(b) 4
(c) 6
(d) 8.
Answer: (b) 4
Hint:
Number of zeros at the end of the number 100 = 2
∴ Number of zeros at the end of the square of the number 100 = 2 × 2 = 4
Q. What will be the number of zeros in the square of the number 50 ?
(a) 1
(b) 2
(c) 3
(d) 4.
Answer: (b) 2
Hint:
Number of zeros at the end of the number 50 = 1
∴ Number of zeros at the end of the square of the number 50 = 2 × 1 = 2.
Q. What will be the number of zeros in the square of the number 9000 ?
(a) 2
(b) 3
(c) 4
(d) 6.
Answer: (d). 6
Hint:
Number of zeros at the end of the number 9000 = 3
∴ Number of zeros at the end of the square of the number 9000 = 2 × 3 = 6.
Q. The square of which of the following numbers will be even ? 11, 111, 1111, 112
(a) 11
(b) 111
(c) 1111
(d) 112.
Answer: (d). 112
Hint:
- 112 is even
- Its square will be even
Q. The square of which of the following numbers will be odd ? 10, 100, 1000, 99
(a) 10
(b) 100
(c) 1000
(d) 99.
Answer: (d). 99
Hint:
- 99 is odd
- Its square will be odd.
Q. The square of which of the following numbers will be even ? 21, 27, 35, 50
(a) 21
(b) 27
(c) 35
(d) 50
Answer: (d) 50
Hint:
∵ 50 is even.
∴ Its square will be even
Q. The square of which of the following numbers will be odd ?
(a) 42
(b) 54
(c) 66
(d) 81.
Answer: (d) 81
Hint:
- 81 is odd
- Its square will be odd.
Q. How many natural numbers he between 8² and 9² ?
(a) 16
(b) 17
(c) 18
(d) 19.
Answer: (a) 16
Hint: (2 × 8 = 16)
Q. How many natural numbers lie between 12² and 13² ?
(a) 20
(b) 22
(c) 24
(d) 26.
Answer: (c) 24
Hint: (2 × 12 = 24 )
Q. How many non square numbers lie between the pair of numbers 80² and 81² ?
(a) 162
(b) 160
(c) 161
(d) 164.
Answer: (b) 160
Hint: (2 × 80 = 160.)
Q. How many non square numbers he between the pair of numbers 36² and 37² ?
(a) 36
(b) 37
(c) 74
(d) 72.
Answer: (d) 72
Hint: (2 × 36 = 72)
Q. How many non square numbers he between the pair of numbers 500² and 501² ?
(a) 1000
(b) 999
(c) 1001
(d) 1002
Answer: (a) 1000
Hint: (2 × 500 = 1000.)
Q. Express the square number 5² as the sum of two consecutive integers.
(a) 12 + 13
(b) 10 + 15
(c) 9 + 16
(d) 20 + 5.
Answer: (a) 12 + 13
Q. Express 9² as the sum of two consecutive integers.
(a) 40 + 41
(b) 50 + 31
(c) 36 + 45
(d) 72 + 9.
Answer: (a) 40 + 41
Q. Express 7² as the sum of two consecutive integers.
(a) 40 + 9
(b) 24 + 25
(c) 36 + 13
(d) 32 + 17.
Answer: (b) 24 + 25
Q. The unit digit number 132 is in the square of the
(a) 1
(b) 2
(c) 3
(d) 4
Answer: (d) 4
Q. The unit digit in the square of the number 1000 is
(a) 1
(b) 0
(c) 2
(d) none of these.
Answer: (b) 0
Hint: (0 × 0 = 0.)
Q. The unit digit in the square of the number 1111 is
(a) 1
(b) 2
(c) 3
(d) 4.
Answer: (a) 1
Hint: (1 × 1 = 1.)
Q. The unit digit in the square of the number 1333 is
(a) 3
(b) 6
(c) 9
(d) 1.
Answer: (c) 9
Hint: (3 × 3 = 9.)
Q. The unit digit in the square of the number 2644 is
(a) 4
(b) 6
(c) 8
(d) 2.
Answer: (b) 6
Hint: (4 × 4 = 16.)
Q. The unit digit in the square of the number 125 is
(a) 1
(b) 2
(c) 5
(d) 6.
Answer: (c) 5
Hint: (5 × 5 = 25)
Q. The unit digit in the square of the number 166 is
(a) 2
(b) 4
(c) 6
(d) 8.
Answer: (c) 6
Hint: (6 × 6 = 36.)
Q. The unit digit in the square of the number 27 is
(a) 7
(b) 2
(c) 5
(d) 9.
Answer: (d) 9
Hint: (7 × 7 = 49.)
Q. The unit digit in the square of the number 78 is
(a) 1
(b) 2
(c) 3
(d) 4.
Answer: (d) 4
Hint: (8 × 8 = 64.)
Q. The unit digit in the square of the number 209 is
(a) 1
(b) 2
(c) 0
(d) 9.
Answer: (a) 1
Hint: (9 × 9 = 81)
Q. Which of the following is not a Pythagorean triplet ?
(a) 3, 4, 5
(b) 6, 8, 10
(c) 5, 12, 13
(d) 2, 3, 4.
Answer: (d) 2, 3, 4.
Hint: (2² + 3² ≠ 4².)
Q. If 102 = 100, then the square root of 100 is
(a) 1
(b) 10
(c) 100
(d) 1000.
Answer: (b) 10
Q. If 252 = 625, then the square root of 625 is
(a) 5
(b) 25
(c) 125
(d) 625.
Answer: (b). 25
Q. What could be the possible one’s digit of the square root of 625 ?
(a) 2
(b) 3
(c) 4
(d) 5.
Answer: (d) 5.
Hint: (5 × 5 = 25.)
Q. What could be the possible one’s digit of the square root of 121 ?
(a) 1, 9
(b) 3, 4
(c) 6, 7
(d) 7, 8.
Answer: (a). 1, 9
Hint:
1 × 1 = 1
9 × 9 = 81.
Q. What could be the possible one’s digit of the square root of 576 ?
(a) 4, 6
(b) 5, 7
(c) 1, 8
(d) 2, 9.
Answer: (a). 4, 6
Hint:
4 × 4 = 16
6 × 6 = 36.
Q. What could be the possible one’s digit of the square root of 676 ?
(a) 4, 6
(b) 5, 7
(c) 1, 8
(d) 2, 9.
Answer: (a). 4, 6
Hint:
4 × 4 = 16
6 × 6 = 36.
Q. The smallest number by which 32 should be multiplied so as to get a perfect square is
(a) 2
(b) 3
(c) 4
(d) 8
Answer: (a). 2
Hint: (32 × 2 = 64 = 8².)
Q. The smallest number by which 48 should be multiplied so as to get a perfect square is
(a) 2
(b) 3
(c) 4
(d) 5.
Answer: (b). 3
Hint: (48 × 3 = 144 = 12²)
Q. The smallest number by which 45 should be multiplied so as to get a perfect square is
(a) 2
(b) 3
(c) 5
(d) 7.
Answer: (c). 5
Hint: (45 × 5 = 225 = 15²)
Q. The smallest number by which 54 should be multiplied so as to get a perfect square is
(a) 2
(b) 3
(c) 4
(d) 6
Answer: (d). 6
Hint: (54 × 6 = 324 = 18².)
Q. The smallest number by which 28 should be multiplied so as to get a perfect square is
(a) 2
(b) 4
(c) 3
(d) 7.
Answer: (d). 7
Hint: (28 × 7 = 196 = 14²)
Q. The smallest number by which 1000 should be multiplied so as to get a perfect square is
(a) 5
(b) 10
(c) 4
(d) 8.
Answer: (b). 10
Hint: (1000 × 10 = 10000 = 100²)
Q. The smallest number by which 128 should be divided so as to get a perfect square is
(a) 2
(b) 3
(c) 4
(d) 8.
Answer: (a). 2
Hint: (128 ÷ 2 = 64 = 8²)
Q. The smallest number by which 48 should be divided so as to get a perfect square is
(a) 2
(b) 3
(c) 4
(d) 6.
Answer: (b). 3
Hint: (48 ÷ 3 = 16 = 4²)
Q. The smallest number by which 125 should be divided so as to get a perfect square is
(a) 3
(b) 5
(c) 25
(d) 125.
Answer: (b). 5
Hint: (125 ÷ 5 = 25 = 5²)
Q. The smallest number by which 150 should be divided so as to get a perfect square is
(a) 4
(b) 2
(c) 5
(d) 6.
Answer: (d) 6.
Hint: (150 ÷ 6 = 25 = 5²)
Q. The smallest number by which 112 should be divided so as to get a perfect square is
(a) 6
(b) 4
(c) 3
(d) 7.
Answer: (d). 7
Hint: (112 ÷ 7 = 16 = 4²)
Q. The smallest number by which 1000 should be divided so as to get a perfect square is
(a) 5
(b) 10
(c) 100
(d) 1000.
Answer: (b). 10
Hint: (1000 ÷ 10 = 100 = 10²)
Q. The smallest 3-digit perfect square is
(a) 999
(b) 100
(c) 961
(d) 125.
Answer: (b). 100
Hint: (100 = 10²)
Q. The number of digits in the square root of 62500 is
(a) 1
(b)2
(c) 3
(d) 4
Answer: (c). 3
Q. The number of digits in the square root of 441 is
(a) 1
(b)2
(c) 3
(d) 4.
Answer: (b). 2
Q. The number of digits in the square root of 100 is
(a) 1
(b)2
(c) 3
(d) 4.
Answer: (b). 2
Q. Find the length of the side of a square whose area is 100 cm².
(a) 5 cm
(b) 10 cm
(c) 100 cm
(d) 4 cm.
Answer: (b). 10 cm
Q. The students of class VIII of a school donated Rs 10000 in all, for Prime Minister’s National Relief Fund. Each student donated as many rupees as the number of students in the class. The number of students in the class is
(a) 10
(b) 100
(c) 1000
(d) 10000
Answer: (b). 100
Q. Which of the following is a perfect square?
A. 1057
B. 625
C. 7928
D. 64000
Answer: B. 625
Explanation: The natural numbers which end with 0, 2, 3, 7 and 8 are not perfect squares. Hence, 625 is a perfect square.
(25 x 25 = 625)
Q. Which of the following will have 6 at unit place?
A. 192
B. 112
C. 242
D. 132
Answer: C. 242
Explanation: 242 = 24 x 24 = 576
Q. If 5278 is squared, then what will be at unit place?
A. 8
B. 7
C. 6
D. 4
Answer: D. 4
Explanation: If we square the unit digit of the number 5278 we get:
82 = 64
Hence, at the unit place of 52782 the number is 4.
Q. What will be the number of zeros in square of 400?
A. 2
B. 3
C. 4
D. 6
Answer: C. 4
Explanation: 4002 = 400 x 400 = 160000
Q. How many natural numbers lie between 92 and 102?
A. 17
B. 18
C. 19
D. 20
Answer: B. 18
Explanation: The number of natural numbers between n2 and (n+1)2 is equal to 2n.
Here, n = 9
Therefore, 2n = 2 x 9 = 18
Q. What is the sum of the first four odd natural numbers?
A. 16
B. 17
C. 18
D. 20
Answer: A. 16
Explanation: The sum of the first odd natural numbers = 1+3+5+7 = 16
Q. The value of 92 – 1 is equal to:
A. 81
B. 80
C. 79
D. None of the above
Answer: B. 80
Explanation: 92-1 = 81 – 1 = 80
Q. The sum of 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 +19 is:
A. 121
B. 120
C. 100
D. 110
Answer: C. 100
Explanation: Sum of n odd numbers = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 +19 =100
Q. The square of 42 is:
A. 1764
B. 1664
C. 1564
D. 1504
Answer: A. 1764
Explanation: 422 = (40 + 2)2
= (40+2) (40+2)
= 40(40 + 2) + 2(40 + 2)
= 402 + 40 x 2 + 2 x 40 + 22
= 1600 + 80 + 80 + 4
= 1764
Q. The Pythagorean triples whose smallest number is 8:
A. 8, 16 17
B. 8, 17, 18
C. 8, 15, 17
D. 8, 15, 16
Answer: C. 8, 15, 17
Explanation: The general form of Pythagorean triplets is 2m, m2-1, m2+1
Given, 2m = 8
So, m = 4
m2 – 1= 42-1 = 16-1 = 15
m2+1=42+1= 16+1 = 17
Q. Which of the following is a perfect square? 32, 66, 81, 101.
A. 32
B. 66
C. 81
D. 101
Answer: C. 81
Explanation: 81 = 9 x 9 = 92
Q. A perfect square that lies between 40 and 50 is:
A. 42
B. 45
C. 46
D. 49
Answer: D. 49
Explanation: 49 is a perfect square.
49 = 7 x 7 = 72
Q. Which of the following is not a square number?
A. 4
B. 9
C. 24
D. 100
Answer: C. 24
Explanation: 24 is not a square number. It cannot be written as n2, where n is any natural number.
Q. Find the greatest four-digit number that is a perfect square.
A. 9990
B. 9801
C. 9999
D. None of these
Answer: B. 9801
Explanation: 9801 is a perfect square.
9801 = 99 x 99 = 992
Q. The square of which of these will have 6 at the unit place?
A. 172
B. 162
C. 152
D. 192
Answer: B. 162
Explanation: The square of 16,
162 = 16 x 16 = 256
Hence, the unit place of the number has 6.
Q. The square of which of the following number will be an even number?
A. 31
B. 69
C. 67
D. 38
Answer: D. 38
Explanation: If the square of unit place digit is an even number, then the square of the number will also be an even number.
Square of 8 = 82 = 64
Since, 4 is an even number, thus, square of 38 is also an even number.
Q. How many zeros are there for the square of 200?
A. 2
B. 3
C. 4
D. 6
Answer: C. 4
Explanation: Square of 200 is:
2002 = 200 x 200 = 2 x 100 x 2 x 100 = 4 x 10000 = 40000
Hence, there are four zeros.
Q. What will be the unit digit of square of 35789?
A. 1
B. 9
C. 3
D. 8
Answer: A. 1
Explanation: The square of 35789 will be having 1 at its unit place
Square of unit place digit of 35789 => 9 x 9 = 81
Since, the square of the unit place digit has 1 at its unit place, thus the number will also have the same digit.
Q. can be expressed as the sum of how many same odd numbers?
A. 5
B. 7
C. 9
D. 11
Answer: B. 7
Explanation: 7 + 7 + 7+7+7+7 +7 = 49
This proves 7 times of 7 is equal to 49
Or 72 = 49
Q. What is the length of side of a square, if the area of square is 441 cm2?
A. 21 cm
B. 29 cm
C. 31 cm
D. 39 cm
Answer: A. 21
Explanation: Area of a square = 441 cm2
By the formula, we know that;
Area of a square = side2
441 = side2
Side = √441 = 21
Therefore, length of side of square is 21 cm.
b) 8, 17, 18
c) 8, 15, 17
d) 8, 15, 16
Answer: (c). 8, 15, 17
Explanation: The general form of Pythagorean triplets is 2m, m2-1, m2+1
Given, 2m = 8
So, m = 4
m2 – 1= 42-1 = 16-1 = 15
m2+1=42+1= 16+1 = 17
Q. What will be the number of zeros in square of 400?
a) 2
b) 3
c) 4
d) 6
Answer: (c). 4
Explanation: 4002 = 400 x 400 = 160000
Q. How many natural numbers lie between 92 and 102?
a) 17
b) 18
c) 19
d) 20
Answer: (b). 18
Explanation: The number of natural numbers between n2 and (n+1)2 is equal to 2n.
Here, n = 9
Therefore, 2n = 2 x 9 = 18
Q. What is the sum of first four odd natural numbers?
a) 16
b) 17
c) 18
d) 20
Answer: (a). 16
Explanation: The sum of first odd natural numbers = n 2
Here, n = 4
So, n2 = 42 = 16
Q. The value of 92 – 1 is equal to:
a) 81
b) 80
c) 79
d) None of the above
Answer: (b). 80
Explanation: 92-1 = 81 – 1 = 80
Q. The sum of 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 +19 is:
a) 121
b) 120
c) 100
d) 110
Answer: (c). 100
Explanation: Sum of n odd numbers = n2
102 = 100
Q. The square of 42 is:
a) 1764
b) 1664
c) 1564
d) 1504
Answer: (a). 1764
Explanation: 422 = (40 + 2)2 = 40(40 + 2) + 2(40 + 2)
= 402 + 40 x 2 + 2 x 40 + 22
= 1600 + 80 + 80 + 4
= 1764
Q. What will be the value of „ x‟ in Pythagorean triplet (6,8, x)?
(a) 5
(b) 7
(c)10
(d) 11
Answer: (c). 10
Q. By which smallest number 90 must be multiplied so as to make it a perfect square?
(a) 10
(b) 2
(c) 5
(d) 3
Answer: (a).10
Q. By which smallest number 48 must be divided so as to make it a perfect square ?
(a) 2
(b) 3
(c) 6
(d) 4
Answer: (b). 3
Q. which smallest number should be added to 80 so as to make it a perfect square?
(a) 2
(b) 3
(c) 1
(d) 4
Answer: (c). 1
Q. Which least number should be subtracted from 629 so as to get a perfect square?
(a) 4
(b) 5
(c) 6
(d) 3
Answer: (a). 4
Q. The square root of 1.21 is
(a) 1.1
(b) 11
(c) 21
(d) 2.1
Answer: (a). 1.1
Q. What is the smallest square number which is divisible by each of the numbers 6,9 and 15 ?
(a) 900
(b) 810
(c) 630
(d) 720
Answer: (a).900
Q. The square of 1.2 is
(a) 144
(b) 1.44
(c) 14.4
(d) 2.4
Answer: (b). 1.44
Q. What is the length of the diagonal of a rectangle having dimensions 3cm and 4cm?
(a) 5
(b) 7
(c) 1
(d) 4
Answer: (a). 5
Q. What will be the length of third side of a right angled triangle whose hypotenuse is 5cm and one of the side is 3 cm?
(a) 2
(b) 3
(c) 4
(d) 5
Answer: (c). 4
Q.
a) 5/12
b) 7/12
c) 25/44
d) none of these
Answer: (a). 5/12
Q.
a) 1
b) 14
c) none of these
d) cannot be determined
Answer: a). 1
Q. The square root of 71 × 72 × 73 × 74 + 1 is
a) 5255
b) 9625
c) 9375
d) 5625
Answer: a). 5255
Q. If a square number ends in 6, the preceding figure is
a) an odd number
b) a composite number
c) an even number
d) a prime number
Answer: a). an odd number
Q.
a) – 1
b) ± 2
c) + 1
d) none
Answer: -1
Q. The value of (501)2 – (500)2 is
a) 1001
b) 1
c) 101
d) none of these
Answer: (a). 1001
Q. Which of the following is a Pythagorean triplet?
a) (6, 8, 10)
b) (5, 12, 18)
c) (3, 4, 7)
d) none of these
Answer: (a). (6, 8, 10)
Q. The value of 1 + 3 + 5 + 7 + 9 + ….. + 25 is
a) 169
b) 625
c) 196
d) 225
Answer: a). 169
We take the first term , last term , common difference and the number of terms .
Q. The smaller number by which 396 must be multiplied so that the product becomes a perfect square is
a) 11
b) 2
c) 5
d) 3
Answer: (a). 11
Q. The value of √99 X √396 is
a) 198
b) none of these
c) 208
d) 254
Answer: (a) 198
Q. Square root of 0.081/0.0064 X 0.484/6.25 X 2.5/12.1 is
a) 0.45
b) 0.95
c) 0.75
d) 0.75
Answer: (a) 0.45
Q. The value of 1+√0.01 / 1−√0.01 is close to
- a) 1.6
- b) 0.6
- c) 1.1
- d) 1.7
Answer: (a) 1.6
Q.
a) lies between 1 and 2
b) equals 1
c) lies between 0 and 1
d) is grater than 2
Answer: lies between 1 and 2
Q.
- a) 9
- b) 0
- c) – 7
- d) 2
Answer: (a). 9
Q.
a) 6
b) 6.4
c) 3
d) 5
Answer: (a). 6
Q. A number added to its square gives 56. The number is
a) 7
b) 9
c) 12
d) 8
Answer: (a). 7
Q. The least number which must be subtracted from 6156 to make its perfect square is
a) 72
b) 82
c) 52
d) 62
Answer: (a) .72
Q. A four digit perfect square number whose first two digits and last two digits taken separately are also perfect square numbers is
a) 1681
b) 3664
c) 1636
d) 6481
Answer: (a) 1681