MCQ on Squares and Square Roots for Class 8
Class 8 Maths Chapter 6 Squares and Square Roots MCQ
MCQ of Squares and Square Roots Class 8
I. Choose the correct answer.
Question 1.
How many perfect square numbers are there in between 1001 to 100001 that are ending with 2 ?
A) 99000
B) 9000
C) 99
D) none
Answer:
D) none
Question 2.
(A B) is a perfect square, A1 is another maximum perfect square that is below 100. Then square root of (AB) is _________ .
A) 10
B) 9
C) 8
D) 6
Answer:
B) 9
Question 3.
Total number of perfect squares below 100 are _________ .
A) 9
B) 10
C) 25
D) 36
Answer:
A) 9
Question 4.
Which of the following is not a perfect square ?
A) ×××× 2
B) ×××× 3
C) ×××× 7
D) All the above
Answer:
D) All the above
Question 5.
A number ×××× P is a perfect square. Then the value of ‘P’
P) may be 4
Q) may be 5
R) may be 7
S) will not be 0
T) may be 3
A) P, Q are true
B) P, Q are false
C) R, S, T are false
D) ‘A’ and ’C’
Answer:
A) P, Q are true
Question 6.
Which of the following is a perfect square ?
A) 7225
B) 1849
C) 5476
D) All the above
Answer:
D) All the above
Question 7.
Which of the following is not a perfect square ?
A) 8100
B) 12321
C) 2401
D) none of the above
Answer:
D) none of the above
Question 8.
‘AB’ is the maximum two digit number where B = 7, then the square of (AB) = ________
A) 997
B) 9409
C) 9909
D) 9999
Answer:
B) 9409
Question 9.
The square of ‘pq’ has 6 in its units digit, then the value of ’q’ is ________
A) 2 or 8
B) 4 or 6
C) 5 or 0
D) 3 or 9
Answer:
B) 4 or 6
Question 10.
Difference between first two perfect square numbers below 10009 is ________
A) 1
B) 4
C) 9
D) 3
Answer:
D) 3
Question 11.
Sum of first ________odd numbers is 400
A) 20
B) 25
C) 15
D) 18
Answer:
A) 20
Question 12.
1 + 3 + 5 + …………. + p = 625, then p = ?
A) 25
B) 50
C) 49
D) 51
Answer:
C) 49
Question 13.
How many natural numbers are there in between 912 and 922 ?
A) 184
B) 182
C) 180
D) 90
Answer:
B) 182
Question 14.
What are two perfect squares that 160 natural numbers exist in between them?
A) 6400, 6561
B) 80, 240
C) 49,209
D) no such numbers exist.
Answer:
A) 6400, 6561
Question 15.
Square root of 123454321 is __________ .
A) 1111
B) 11111
C) 111111
D) 111
Answer:
B) 11111
Question 16.
Square of 6667 = _________ .
A) 4448889
B) 4488889
C) 4888889
D) 44448889
Answer:
D) 44448889
Question 17.
Which of the following can be expressed as sum of two consecutive integers?
A) 62
B) 82
C) 102
D) 112
Answer:
D) 112
Question 18.
Square of __________ numbers can only be expressed as sum of two consecutive integers.
A) negative integers
B) even
C) odd
D) all natural
Answer:
C) odd
Question 19.
(a5)2 = (_____x_____) 100 + (25) fill the blank.
A) a(a + 1)
B) a(a + 2)
C) a(a + 3)
D) none
Answer:
A) a(a + 1)
Question 20.
(p3 x p7) = (_________) x 100 + (21) Fill the balnk.
A) p(p + 7)
B) (p + 3) (p + 7)
C) p(p + 1)
D) none
Answer:
C) p(p + 1)
Question 21.
Which of the following is not a Ppythagorean triplet ?
A) 5, 12, 13
B) 3, 4, 5
C) 6, 8, 10
D) 1, 2, 3
Answer:
D) 1, 2, 3
Question 22.
\(\sqrt{169}\) = ________ .
A) 13
B) -13
C) ±13
D) 23
Answer:
C) ±13
Question 23.
A number is factorised as 4 × 6 × 2 × 6. So, what is the least number to be multiplied it to make it a perfect square ?
A) 4
B) 4 × 2
C) 2
D) 6
Answer:
C) 2
Question 24.
‘P’ is factorised as 5 × 7 × 9 × 3 × 3 × 7 × 6 × 5. So, what makes ‘P’ a perfect square ?
A) multiplying by 6
B) dividing by 6
C) A or B
D) dividing by 3
Answer:
C) A or B
Question 25.
\(\sqrt{1296}\) + \(\sqrt{729}\) – √x = 0 ; So, (x) = ________ .
A) 63
B) 6393
C) 3699
D) 3969
Answer:
D) 3969
For this A, R type questions, from 26 to 30. Choose the correct answer from the options given below.
A) Both A, R are correct and ‘R’ is the correct explanation of ‘A’.
B) Both A, R are true but ‘R’ is not the correct explanation of ‘A’.
C) ‘A’ is true but ‘R’ is false.
D) ‘R’ is true but ‘A’ is false.
Question 26.
Assertion (A) : The number of zeros in the square of 3000 is 6.
Reason (R) : The number of zeros in the square of a number having ‘n’ zeros is ‘2n’.
Answer:
A) Both A, R are correct and ‘R’ is the correct explanation of ‘A’.
Question 27.
Assertion (A) : \(\sqrt{12321}\) = 111
Reason (R) : \(\sqrt{444889}\) = 667
Answer:
B) Both A, R are true but ‘R’ is not the correct explanation of ‘A’.
Question 28.
Assertion (A) : 3, 4, 5 is a Pythagorean triplet.
Reason (R) : In Pythagorean triplets sum of squares of two little numbers is equal to square of third number.
Answer:
A) Both A, R are correct and ‘R’ is the correct explanation of ‘A’.
Question 29.
Assertion (A) : The unit digit in the square of 285 is 4.
Reason (R) : The unit digit in the square of 171 is 1.
Answer:
D) ‘R’ is true but ‘A’ is false.
Question 30.
Assertion (A) : Square of an even number is always an even.
Reason (R) : Square of an odd number is always an odd.
Answer:
B) Both A, R are true but ‘R’ is not the correct explanation of ‘A’.
Question 31.
A number equals 2 × 2 × 3 × 3 × 5 × 5. What will be the square root of the
A) 20
B) 25
C) 30
D) 35
Answer:
C) 30
Question 32.
The square root of 50625 lies between
A) 20 and 30
B) 70 and 80
C) 200 and 300
D) 700 and 800
Answer:
C) 200 and 300
Question 33.
Given below is the prime factorisation of a number.
6534 = 2 × 3 × 3 × 3 × 11 × 11
What is the smallest number by which you can DIVIDE 6534 so that the quotient is a perfect square ?
A) 2
B) 3
C) 6
D) 11
Answer:
C) 6
Question 34.
Given below is an expression.
\(\sqrt{0.0081}\) – \(\sqrt{0.36}\) + \(\sqrt{0.64}\) – \(\sqrt{0.0016}\)
A) \(\sqrt{0.2865}\)
B) 0.25
C) 0.5
D) 0.7
Answer:
B) 0.25
Question 35.
Which of the following is not a perfect square number?
A) 256
B) 81
C) 125
D) 225
Answer:
C) 125
Question 36.
Smallest square number that is divisible by 4 and 6 is __________
A) 16
B) 36
C) 12
D) 64
Answer:
B) 36
Question 37.
Number of zeroes in the square of 200
A) 2
B) 3
C) 4
D) 5
Answer:
A) 2
Question 38.
If 12 + 22 + 22 = 32
22 + 32 + 62 = 72
32 + 42 + 122 = 132 then 42 + 52 + 202 = ________
A) 172
B) 192
C) 212
D) 232
Answer:
C) 212
II. Fill in the blanks.
1. \(\sqrt{23.04}\) = __________ .
Answer:
4.8
2. Number of digits in \(\sqrt{20,857,489}\) = __________ .
Answer:
4
3. The least number to be subtracted from 3250 to get a perfect square is __________ .
Answer:
114
4. The least number to be added to 2601 to make it perfect square __________ .
Answer:
0
5. Every student, whose Roll is odd (from 1) collected an amount equal to their roll number. If the total collection is 625. Then the roll number of last candidate who gave donation is __________ .
Answer:
51
6. In the given figure, find the side \(\overline{\mathrm{AB}}\) = __________ .
Answer:
12
7. \(\sqrt{100000000 \ldots \ldots . . . . .(14 \text { zeros })}\) = ___________ .
Answer:
100……(7 zeros)
8. One’s digit in (52698)2 + (78601)2 – (23255)2 = __________ .
Answer:
0
9. A number ends with __________ or __________ will never become a perfect square.
Answer:
2, 3, 7 or 8
10. The value of \(\sqrt{169}\) is.
Answer:
13
III. Match the following.
Question 1.
| A | B |
| 1) \(\sqrt{(123689)^2}\) = | a) 180 + 181 |
| 2) 442 = | b) 28 |
| 3) 196 …………., 225 (numbers in gap ?) | c) 1 |
| 4) \(\sqrt{152 \mathrm{P}}\)= 39, So, P = ? | d) ± 123689 |
| 5) 192 = _________ | e) 1936 |
Answer:
(1, d) (2, e) (3, b) (4, c) (5, a)
| A | B |
| 1) \(\sqrt{(123689)^2}\) = | d) ± 123689 |
| 2) 442 = | e) 1936 |
| 3) 196 …………., 225 (numbers in gap ?) | b) 28 |
| 4) \(\sqrt{152 \mathrm{P}}\)= 39, So, P = ? | c) 1 |
| 5) 192 = _________ | a) 180 + 181 |
Question 2.
| A | B |
| 1) (p5)2 = __________ | a) 1246642 |
| 2) 5, 13 and ’k’ are Pythagorean triplet, then k = _________ | b) 12 |
| 3) √1 + √4 = _______ | c) + 1 or -1 or + 3 or -3 |
| 4) \(\sqrt{7561+P}\) is an integer, then possible least value of ’P’ = __________ | d) [P × (P + 1)] 100 + (25) |
| 5) 1112 + 1112 = ______________ | e) 8 |
Answer:
(1, d) (2, b) (3, c) (4, e) (5, a)
| A | B |
| 1) (p5)2 = __________ | d) [P × (P + 1)] 100 + (25) |
| 2) 5, 13 and ’k’ are Pythagorean triplet, then k = _________ | b) 12 |
| 3) √1 + √4 = _______ | c) + 1 or -1 or + 3 or -3 |
| 4) \(\sqrt{7561+P}\) is an integer, then possible least value of ’P’ = ________ | e) 8 |
| 5) 1112 + 1112 = ________ | a) 1246642 |