CBSE Class 8 Mathematics Square And Square Roots Worksheet Set 02

Question. What is the least perfect square which is divisible by 2, 4 and 6 ?
(A) 36
(B) 64
(C) 16
(D) 18
Answer : A

Question. What is the number of digits in the square root of 390625 ?
(A) 4
(B) 6
(C) 5
(D) 3
Answer : D

Question. Find the approximate value of 1 + √0.01 / 1-√0.1
(A) 0.6
(C) 1.6
(B) 1.1
(D) 1.7
Answer : C

Question. If x * y = √x² + y² , find the value of (1 * 2√2)(1 * -2√2)
(A) -7
(B) 0
(C) 2
(D) 9
Answer : D

Question. Evaluate

(A) 3
(B) 6
(C) 5
(D) 6.
Answer : B

Question. What is the least perfect square exactly divisible by each of the numbers 6, 9, 15 and 20?
(A) 3600
(B) 900
(C) 400
(D) 225
Answer : B

Question. The sides of a rectangular field are 80 m and 18 m respectively. What is the length of its diagonal ?
(A) 84 m
(B) 98 m
(C) 82m
(D) 86 m 
Answer : C

Question. What is the value of (501)²- (500)² ?
(A) 1
(B) 101
(C) 1001
(D) 100
Answer : C

Question. Which of the following is a Pythagorean triplet?
(A) (6, 8, 1 0)
(C) (5, 12, 18)
(B) (3, 4, 7)
(D) (2, 3, 6)
Answer : A

Question. What is the value of 1 + 3 + 5 + 7 + 9 +...............+ 25?
(A) 196
(B) 625
(C) 225
(D) 169
Answer : D

Question. What is the smallest number by which 396 must be multiplied so that the product is a perfect square ?
(A) 5
(C) 3
(B) 11
(D) 2
Answer : B

Question. Find the square root of 0.081/0.0064 x 0.484/6.25 x 2.5/12.1
(A) 0.45
(C) 0.95
(B) 0.75
(D) 0.99
Answer : A

Question. What is the least number which must be subtracted from 2509 to make it a perfect square ?
(A) 6
(B) 9
(C) 12
(D) 14 
Answer : B

Question. What is the square root of 42(583/1369)?
(A) 6(19/37)
(B) 4(2/11)
(C) 7(2/121)
(D) 6(12/37)
Answer : A

Question. If √1 + 27/169 = 1 + x/13 , what is the value of 'X ' ?
(A) 1
(B) 14
(C) 10
(D) 12
Answer : A

Question. Find the perfect square numbers between
(i) 30 and 40
(ii) 50 and 60
Answer: (i) 36
(ii) There is not any perfect square number between 50 & 60.

Question. Check whether the following numbers can be perfect squares? Give reason.
(i) 1057
(ii) 23453
(iii) 7928
(iv) 222222
(v) 1089
(vi) 2061
Answer: (i) No, because it ends with 7.
(ii) No, because it ends with 3.
(iii) No, because it ends with 8.
(iv) No, because it ends with 2.
(v) Yes, it has 9 at unit place.
(vi) Yes, it has 1 at unit place.

Question. Write five numbers which you cannot decide just by looking at their unit's digit (or one's place) whether they are square numbers or not.
Answer: 169, 38126, 591, 100, 343795. Since 2, 3, 7, 8 are not at ones place, we cannot decide just by looking at the unit digit.

Question. Which of \( 123^2, 77^2, 82^2, 161^2, 109^2 \) would end with digit 1?
Answer: \( 161^2 \) and \( 109^2 \)

Question. Which of the following numbers would have digit 6 at unit place.
(i) \( 19^2 \)
(ii) \( 24^2 \)
(iii) \( 26^2 \)
(iv) \( 36^2 \)
(v) \( 34^2 \)
Answer: \( 24^2, 26^2, 36^2, 34^2 \)

Question. What will be the ‘‘one’s digit’’ in the square of the following numbers?
(i) 1234
(ii) 26387
(iii) 52698
(iv) 99880
(v) 21222
(vi) 9106
Answer: (i) 6
(ii) 9
(iii) 4
(iv) 0
(v) 4
(vi) 6

Question. The square of which of the following numbers would be an odd number/an even number? Why?
(i) 727
(ii) 158
(iii) 269
(iv) 1980
Answer: (i) Odd because the unit place will be 9.
(ii) Even because the unit place will be 4.
(iii) Odd because the unit place will be 1.
(iv) Even because the unit place will be 0.

Question. What will be the number of zeros in the square of the following numbers?
(i) 60
(ii) 400
Answer: (i) Two
(ii) Four

Question. How many natural numbers lie between \( 9^2 \) and \( 10^2 \)? Between \( 11^2 \) and \( 12^2 \)?
Answer: Between \( 9^2 \) and \( 10^2 \), there are 18 natural numbers.
Between \( 11^2 \) and \( 12^2 \), there are 22 natural numbers.

Question. How many non square numbers lie between the following pairs of numbers
(i) \( 100^2 \) and \( 101^2 \)
(ii) \( 90^2 \) and \( 91^2 \)
(iii) \( 1000^2 \) and \( 1001^2 \)
Answer: (i) 200
(ii) 180
(iii) 2000

Question. Find whether each of the following numbers is a perfect square or not?
(i) 121
(ii) 55
(iii) 81
(iv) 49
(v) 69
Answer: (i) Yes
(ii) No
(iii) Yes
(iv) Yes
(v) No

Question. Express the following as the sum of two consecutive integers.
(i) \( 21^2 \)
(ii) \( 13^2 \)
(iii) \( 11^2 \)
(iv) \( 19^2 \)
Answer: (i) \( 21^2 = 441 = 220 + 221 \)
(ii) \( 13^2 = 169 = 84 + 85 \)
(iii) \( 11^2 = 121 = 60 + 61 \)
(iv) \( 19^2 = 361 = 180 + 181 \)

Question. Is it possible that the sum of any two consecutive positive integers is perfect square of a number? Give example to support your answer.
Answer: Yes. Examples:
(i) \( 21^2 = 441 = 220 + 221 \)
(ii) \( 13^2 = 169 = 84 + 85 \)
(iii) \( 11^2 = 121 = 60 + 61 \)
(iv) \( 19^2 = 361 = 180 + 181 \)

Question. Write the square, by any pattern.
(i) 75
(ii) 95
Answer: (i) 5625
(ii) 9025

Question. Find the value of \( 17^2 - 12^2 + 15^2 - 10^2 \)
Answer: 270

Question. What will be the unit digit of the squares of the following numbers?
(i) 81
(ii) 272
(iii) 799
(iv) 3853
(v) 1234
(vi) 26387
(vii) 52698
(viii) 99880
(ix) 12796
(x) 55555
Answer: (i) 1
(ii) 4
(iii) 1
(iv) 9
(v) 6
(vi) 9
(vii) 4
(viii) 0
(ix) 6
(x) 5

Question. The following numbers are obviously not perfect squares. Give reason.
(i) 1057
(ii) 23453
(iii) 7928
(iv) 222222
(v) 64000
(vi) 89722
(vii) 222000
(viii) 505050
Answer: (i) Ends with 7
(ii) Ends with 3
(iii) Ends with 8
(iv) Ends with 2
(v) Contains an odd number of zeros (3 zeros)
(vi) Ends with 2
(vii) Contains an odd number of zeros (3 zeros)
(viii) Contains an odd number of zeros at the end

Question. The squares of which of the following would be odd numbers?
(i) 431
(ii) 2826
(iii) 7779
(iv) 82004
Answer: (i) and (iii)

Question. Observe the following pattern and find the missing digits.
\( 11^2 = 121 \)
\( 101^2 = 10201 \)
\( 1001^2 = 1002001 \)
\( 100001^2 = 1 \dots\dots 2 \dots\dots 1 \)
\( 10000001^2 = \dots\dots\dots\dots\dots\dots\dots \)
Answer: \( 100001^2 = 10000200001 \)
\( 10000001^2 = 100000020000001 \)

Question. Observe the following pattern and supply the missing numbers.
\( 11^2 = 121 \)
\( 101^2 = 10201 \)
\( 10101^2 = 102030201 \)
\( 1010101^2 = \dots\dots\dots\dots\dots\dots\dots^2 = 10203040504030201 \)
Answer: \( 1010101^2 = 10203040504030201 \)

Question. Using the given pattern, find the missing numbers.
\( 1^2 + 2^2 + 2^2 = 3^2 \)
\( 2^2 + 3^2 + 6^2 = 7^2 \)
\( 3^2 + 4^2 + 12^2 = 13^2 \)
\( 4^2 + 5^2 + \_\_^2 = 21^2 \)
\( 5^2 + \_\_^2 + 30^2 = 31^2 \)
\( 6^2 + 7^2 + \_\_^2 = \_\_^2 \)
Answer: 20, 6, 42, 43

Question. Without adding, find the sum.
(i) 1 + 3 + 5 + 7 + 9
(ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19
(iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23
Answer: (i) 25
(ii) 100
(iii) 144

Question. (i) Express 49 as the sum of first 7 odd numbers.
(ii) Express 121 as the sum of first 11 odd numbers.
Answer: (i) 1 + 3 + 5 + 7 + 9 + 11 + 13
(ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21

Question. How many numbers lie between squares of the following numbers?
(i) 12 and 13
(ii) 25 and 26
(iii) 99 and 100
Answer: (i) 24
(ii) 50
(iii) 198

Please click the below link to access CBSE Class 8 Mathematics Worksheet - Square and Square Roots (1)