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## Wednesday, 24 February 2021

### CBSE Class 8 Maths - MCQ and Online Tests - Unit 6 - Squares and Square Roots

#### CBSE Class 8 Maths – MCQ and Online Tests –  Unit 6 – Squares and Square Roots

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#### CBSE Class 8 Maths – MCQ and Online Tests – Unit 6 – Squares and Square Roots

Question 1.
The unit digit in the square of the number 27 is
(a) 7
(b) 2
(c) 5
(d) 9.

Hint:
7 ◊ 7 = 49.

Question 2.
The number of digits in the square root of 62500 is
(a) 1
(6)2
(c) 3
(d) 4.

Hint:
n = 5, $$\frac{n+1}{2}$$ = 3.

Question 3.
The number of digits in the square root of 441 is
(a) 1
(6)2
(c) 3
(d) 4.

Hint:
n = 3, $$\frac{n+1}{2}$$ = 2.

Question 4.
The unit digit in the square of the number 78 is
(a) 1
(b) 2
(c) 3
(d) 4.

Hint:
8 ◊ 8 = 64.

Question 5.
The unit digit in the square of the number 209 is
(a) 1
(b) 2
(c) 0
(d) 9.

Hint:
9 ◊ 9 = 81

Question 6.
Which of the following is a perfect square number ?
(a) 1067
(b) 7828
(c) 4333
(d) 625.

Hint:
Perfect square numbers end with
0, 1, 4, 5, 6 or 9 at unitís place.

Question 7.
Which of the following is a perfect square number ?
(a) 2222
(b) 32543
(c) 888
(d) 10000.

Hint:
Perfect square numbers end with
0, 1, 4, 5, 6 or 9 at unitís place.

Question 8.
Which of 1322, 872, 722 and 2092 would end with digit 1 ?
(a) 1322
(b) 872
(c) 722
(d) 2092.

Hint:
If a number has 1 or 9 in the unitís place, then its square ends in 1.

Question 9.
Which of 1052, 2162, 3332 and 1112 would end with digit 1 ?
(a) 1052
(b) 2162
(c) 3332
(d) 1112.

Hint:
If a number has 1 or 9 in the unitís place, then its square ends in 1.

Question 10.
Which of 172, 342, 252 and 492 would have 6 at unit place ?
(a) 172
(b) 342
(c) 252
(d) 492.

Hint:
If a number has 4 or 6 in the unitís place, then its square ends in 6.

Question 11.
Which of 212, 332, 472 and 362 would have 6 at unit place ?
(a) 212
(b) 332
(c) 472
(d) 362.

Hint:
If a number has 4 or 6 in the unitís place, then its square ends in 6.

Question 12.
What will be the number of zeros in the square of the number 100 ?
(a) 2
(b) 4
(c) 6
(d) 8.

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.

Question 13.
What will be the number of zeros in the square of the number 50 ?
(a) 1
(b) 2
(c) 3
(d) 4.

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.

Question 14.
What will be the number of zeros in the square of the number 9000 ?
(a) 2
(b) 3
(c) 4
(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.

Question 15.
The square of which of the following numbers will be even ?
11, 111, 1111, 112
(a) 11
(b) 111
(c) 1111
(d) 112.

Hint:
? 112 is even
? Its square will be even

Question 16.
The square of which of the following numbers will be odd ?
10, 100, 1000, 99
(a) 10
(b) 100
(c) 1000
(d) 99.

Hint:
? 99 is odd
? Its square will be odd.

Question 17.
The square of which of the following numbers will be even ?
21, 27, 35, 50
(a) 21
(b) 27
(c) 35
(d) 50

Hint:
? 50 is even.
? Its square will be even.

Question 18.
The square of which of the following numbers will be odd ?
(a) 42
(b) 54
(c) 66
(d) 81.

Hint:
? 81 is odd
? Its square will be odd.

Question 19.
How many natural numbers he between 8≤ and 9≤ ?
(a) 16
(b) 17
(c) 18
(d) 19.

Hint:
2 ◊ 8 = 16

Question 20.
How many natural numbers lie between 12≤ and 13≤ ?
(a) 20
(b) 22
(c) 24
(d) 26.

Hint:
2 ◊ 12 = 24.

Question 21.
How many nonsquare numbers lie between the pair of numbers 80≤ and 81≤ ?
(a) 162
(b) 160
(c) 161
(d) 164.

Hint:
2 ◊ 80 = 160.

Question 22.
How many nonsquare numbers he between the pair of numbers 36≤ and 37≤ ?
(c) 36
(b) 37
(c) 74
(d) 72.

Hint:
2 ◊ 36 = 72.

Question 23.
How many nonsquare numbers he between the pair of numbers 500≤ and 501≤ ?
(a) 1000
(b) 999
(c) 1001
(d) 1002.

Hint:
2 ◊ 500 = 1000.

Question 24.
Express the square number 5≤ as the sum of two consecutive integers.
(a) 12 + 13
(b) 10 + 15
(c) 9 + 16
(d) 20 + 5.

Hint:
$$\frac{5^2-1}{2}$$ = 12, $$\frac{5^2+1}{2}$$ = 13

Question 25.
Express 9≤ as the sum of two consecutive integers.
(a) 40 + 41
(b) 50 + 31
(c) 36 + 45
(d) 72 + 9.

Hint:
$$\frac{9^2-1}{2}$$ = 40, $$\frac{5^2+1}{2}$$ = 41

Question 26.
Express 7≤ as the sum of two consecutive integers.
(a) 40 + 9
(b) 24 + 25
(c) 36 + 13
(d) 32 + 17.

Hint:
$$\frac{7^2-1}{2}$$ = 24, $$\frac{5^2+1}{2}$$ = 25

Question 27.
The unit digit number 132 is in the square of the
(a) 1
(b) 2
(c) 3
(d) 4.

Hint:
2 ◊ 2 = 4.

Question 28.
The unit digit in the square of the number 1000 is
(a) 1
(b) 0
(c) 2
(d) none of these.

Hint:
0 ◊ 0 = 0.

Question 29.
The unit digit in the square of the number 1111 is
(a) 1
(b) 2
(c) 3
(d) 4.

Hint:
1 ◊ 1 = 1.

Question 30.
The unit digit in the square of the number 1333 is
(a) 3
(b) 6
(c) 9
(d) 1.

Hint:
3 ◊ 3 = 9.

Question 31.
The unit digit in the square of the number 2644 is
(a) 4
(b) 6
(c) 8
(d) 2.

Hint:
4 ◊ 4 = 16.

Question 33.
The perfect square number out of 2, 3, 4 and 5 is
(a) 2
(b) 3
(c) 4
(d) 5.

Hint:
4 = 2 ◊ 2 = 22.

Question 34.
A perfect square number between 30 and 40 is
(a) 36
(b) 32
(c) 33
(d) 39.

Hint:
36 = 6 ◊ 6 = 62.

Question 35.
Between 50 and 60, the perfect square number is
(a) 56
(b) 55
(c) 54
(d) none.

Hint:
None of 51, 52, …… , 59 is a perfect square.

Question 36.
The unit digit in the square of the number 125 is
(a) 1
(b) 2
(c) 5
(d) 6.

Hint:
5 ◊ 5 = 25.

Question 37.
The unit digit in the square of the number 166 is
(a) 2
(b) 4
(c) 6
(d) 8.

Hint:
6 ◊ 6 = 36.

Question 38.
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.

Hint:
2≤ + 3≤ ? 4≤.

Question 39.
If 102 = 100, then the square root of 100 is
(a) 1
(b) 10
(c) 100
(d) 1000.

Hint:
$$\sqrt{100}$$ = 10

Question 40.
The number of digits in the square root of 100 is
(a) 1
(6)2
(c) 3
(d) 4.

Hint:
n = 3, $$\frac{n}{2}$$ = 2.

Question 41.
Find the length of the side of a square whose area is 100 cm≤.
(a) 5 cm
(6) 10 cm
(c) 100 cm
(d) 4 cm.

Hint:
$$\sqrt{100}$$ = 10 cm.

Question 42.
The students of class VIII of a school donated Rs 10000 in all, for Prime Ministerís 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
(6) 100
(c) 1000
(d) 10000.

Hint:
$$\sqrt{10000}$$ = 100.

Question 43.
What could be the possible oneís digit of the square root of 121 ?
(a) 1, 9
(b) 3, 4
(c) 6, 7
(d) 7, 8.

Hint:
1 ◊ 1 = 1
9 ◊ 9 = 81.

Question 44.
What could be the possible oneís digit of the square root of 361 ?
(c) 1, 9
(b) 3, 4
(c) 6, 7
(d) 7, 8.

Hint:
1 ◊ 1 = 1
9 ◊ 9 = 81.

Question 45.
What could be the possible oneís digit of the square root of 576 ?
(o) 4, 6
(b) 5, 7
(c) 1, 8
(d) 2, 9.

Hint:
4 ◊ 4 = 16
6 ◊ 6 = 36.

Question 46.
What could be the possible oneís digit of the square root of 676 ?
(a) 4, 6
(b) 5, 7
(c) 1, 8
(d) 2, 9.

Hint:
4 ◊ 4 = 16
6 ◊ 6 = 36.

Question 47.
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.

Hint:
32 ◊ 2 = 64 = 8≤.

Question 48.
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.

Hint:
48 ◊ 3 = 144 = 12≤.

Question 49.
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.

Hint:
45 ◊ 5 = 225 = 15≤.

Question 50.
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.

Hint:
54 ◊ 6 = 324 = 18≤.

Question 51.
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.

Hint:
28 ◊ 7 = 196 = 14≤.

Question 52.
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.

Hint:
1000 ◊ 10 = 10000 = 100≤.

Question 53.
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.

Hint:
128 ˜ 2 = 64 = 8≤.

Question 54.
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.

Hint:
48 ˜ 3 = 16 = 4≤.

Question 55.
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.

Hint:
125 ˜ 5 = 25 = 5≤.

Question 56.
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.

Hint:
150 ˜ 6 = 25 = 5≤.

Question 57.
The smallest number by which 112 should be divided so as to get a perfect square is
(a)6
(6) 4
(c) 3
(d) 7.

Hint:
112 ˜ 7 = 16 = 4≤.

Question 58.
The smallest number by which 1000 should be divided so as to get a perfect square is
(a) 5
(6) 10
(c) 100
(d) 1000.

Hint:
1000 ˜ 10 = 100 = 10≤.

Question 59.
The smallest 3-digit perfect square is
(a) 999
(6) 100
(c) 961
(d) 125.

Hint:
100 = 10≤.

Question 60.
If 252 = 625, then the square root of 625 is
(a) 5
(b) 25
(c) 125
(d) 625.

Hint:
$$\sqrt{625}$$ = 25

Question 61.
What could be the possible oneís digit of the square root of 625 ?
(a) 2
(b) 3
(c) 4
(d) 5.

Hint:
5 ◊ 5 = 25.

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