CBSE Class 8 Mathematics Square And Square Roots Worksheet Set 03

Question. Which of the following is a four digit perfect square number whose first two dig its and last two digits taken separately are also perfect squares ?
(A) 1681
(B) 1636
(C) 3664
(D) 6481
Answer : A

Question. If √16/49 = x/49 , find the value of 'x:
(A) 4
(B) 7
(C) 16
(D) 28
Answer : D

Question. Evaluate 36.1/102.4
(A) -32
(B) 72
(C) 19/32
(D) 29/62
Answer : C

Question. A group of students decided to collect as many rupees from each member of the group as is the number of members. If the total collection amounts to ~ 2209, what is the number of members in the group?
(A) 37
(B) 47
(C) 107
(D) 43
Answer : B

Question. Find the value of the expression √0.0009 + √0.01
(A) 3
(B) 0.3
(C) 1/3
(D) 0.9
Answer : B

Question. A general wishes to draw up his 36562 soldiers in the form of a solid square. After arranging them, he found that some of them are left over. How many are left?
(A) 36
(B) 65
(C) 81
(D) 97
Answer : C

Question. Find the value of √0.16/0.4
(A) 0.2
(B) 0.02
(C) 0.63
(D) 2√5/5
Answer : C

Question. The area of a square field is 80(244/729) sq. m. What is the length of each side of the field?
(A) 8.96 m
(B) 10.26 m
(C) 13.54 m
(D) 9.86 m
Answer : A

Question. If √2ⁿ = 64 , what is the value of 'n' ?
(A) 2
(B) 4
(C) 6
(D) 12
Answer : D

Question. If √2401 = √7^x ,find the value of ·x:
(A) 3
(B) 4
(C) 5
(D) 6
Answer : B

Question. Find the number, which when subtracted from its square results in 12.
(A) 6
(B) 5
(C) 4
(D) 8 
Answer : C

Question. Which of the following is the smallest number of 4 digits, which is not a perfect square?
(A) 1024
(B) 1089
(C) 1000
(D) 1156
Answer : C

Question. If √24 = 4.899, find the value of √8/3·
(A) 0.544
(B) 2.666
(C) 1.633
(D) 1.333
Answer : C

Question. Evaluate √4/3 - √3/4
(A) 1/2√3
(B) - 1/2√3
(C) 1
(D) 5√3/6
Answer : A

Question. Find the value of √0.064
(A) 0.8
(B) 0.08
(C) 0.008
(D) 0.253
Answer : D

Question. A gardener wants to plant 17956 trees and arranges them in such a way that there are as many rows as there are trees in a row. What is the number of trees in a row?
(A) 144
(B) 136
(C) 154
(D) 134
Answer : D

Question. Given x/√2.25 = 550 , find the value of 'x'.
(A) 825
(B) 82.5
(C) 3666.66
(D) 2
Answer : A

Question. Which is the smallest natural number which when added to the difference of squares of 17 and 13 gives a perfect square?
(A) 1
(B) 5
(C) 11
(D) 24
Answer : A

Question. Find the square of the following numbers.
(i) 32
(ii) 35
(iii) 86
(iv) 93
(v) 71
(vi) 46
Answer: (i) 1024
(ii) 1225
(iii) 7396
(iv) 8649
(v) 5041
(vi) 2116

Question. Write a pythagorean triplet whose one member is.
(i) 6
(ii) 14
(iii) 16
(iv) 18
Answer: (i) 6, 8, 10
(ii) 14, 48, 50
(iii) 16, 63, 65
(iv) 18, 80, 82

Question. What could be the possible ‘one’s’ digits of the square root of each of the following numbers?
(i) 9801
(ii) 99856
(iii) 998001
(iv) 657666025
Answer: (i) 1, 9
(ii) 4, 6
(iii) 1, 9
(iv) 5

Question. Without doing any calculation, find the numbers which are surely not perfect squares.
(i) 153
(ii) 257
(iii) 408
(iv) 441
Answer: (i), (ii), (iii)

Question. Find the square roots of 100 and 169 by the method of repeated subtraction.
Answer: 10, 13

Question. Find the square roots of the following numbers by the prime Factorisation Method.
(i) 729
(ii) 400
(iii) 1764
(iv) 4096
(v) 7744
(vi) 9604
(vii) 5929
(viii) 9216
(ix) 529
(x) 8100
Answer: (i) 27
(ii) 20
(iii) 42
(iv) 64
(v) 88
(vi) 98
(vii) 77
(viii) 96
(ix) 23
(x) 90

Question. For each of the following numbers, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained.
(i) 252
(ii) 180
(iii) 1008
(iv) 2028
(v) 1458
(vi) 768
Answer: (i) 7; 42
(ii) 5; 30
(iii) 7; 84
(iv) 3; 78
(v) 2; 54
(vi) 3; 48

Question. For each of the following numbers, find the smallest whole number by which it should be divided so as to get a perfect square. Also find the square root of the square number so obtained.
(i) 252
(ii) 2925
(iii) 396
(iv) 2645
(v) 2800
(vi) 1620
Answer: (i) 7; 6
(ii) 13; 15
(iii) 11; 6
(iv) 5; 23
(v) 7; 20
(vi) 5; 18

Question. The students of Class VIII of a school donated Rs 2401 in all, for Prime Minister's National Relief Fund. Each student donated as many rupees as the number of students in the class. Find the number of students in the class.
Answer: 49

Question. 2025 plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows. Find the number of rows and the number of plants in each row.
Answer: 45 rows; 45 plants in each row

Question. Find the smallest square number that is divisible by each of the number 4,9 and 10.
Answer: 900

Question. Find the smallest square number that is divisible by each of the numbers 8,15 and 20.
Answer: 3600

Question. Find the least number that must be subtracted from 5607 so as to get a perfect square. Also find the square root of the perfect square.
Answer: 131; 74

Question. Find the greatest 5-digit number which is a perfect square.
Answer: 99856

Question. Find the least number that must be added to 1300 so as to get a perfect square. Also find the square root of the perfect square.
Answer: 69

Question. Find the square root of each of the following numbers by Division method.
(i) 2304
(ii) 4489
(iii) 3481
(iv) 529
(v) 3249
(vi) 1369
(vii) 5776
(viii) 7921
(ix) 576
(x) 1024
(xi) 3136
(xii) 900
Answer: (i) 48
(ii) 67
(iii) 59
(iv) 23
(v) 57
(vi) 37
(vii) 76
(viii) 89
(ix) 24
(x) 32
(xi) 56
(xii) 30

Question. Find the number of digits in the square root of each of the following numbers (without any calculation).
(i) 64
(ii) 144
(iii) 4489
(iv) 27225
(v) 390625
Answer: (i) 1
(ii) 2
(iii) 2
(iv) 3
(v) 3

Question. Find the square root of the following decimal numbers.
(i) 2.56
(ii) 7.29
(iii) 51.84
(iv) 42.25
(v) 31.36
Answer: (i) 1.6
(ii) 2.7
(iii) 7.2
(iv) 6.5
(v) 5.6

Question. Find the least number which must be subtracted from each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained.
(i) 402
(ii) 1989
(iii) 3250
(iv) 825
(v) 4000
Answer: (i) 2; 20
(ii) 53; 44
(iii) 1; 57
(iv) 41; 28
(v) 31; 63

Question. Find the least number which must be added to each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained.
(i) 525
(ii) 1750
(iii) 252
(iv) 1825
(v) 6412
Answer: (i) 4; 23
(ii) 14; 42
(iii) 4; 16
(iv) 24; 43
(v) 149; 81

Question. Find the length of the side of a square whose area is \( 441 \text{ m}^2 \).
Answer: 21 m

Question. In a right triangle ABC, \( \angle B = 90^\circ \).
(i) If AB = 6 cm, BC = 8 cm find AC
(ii) If AC = 13 cm, BC = 5 cm find AB
Answer: (i) 10 cm
(ii) 12 cm

Question. A gardener has 1000 plants. He wants to plant these in such a way that the number of rows and the number of columns remain same. Find the minimum number of plants he needs more for this.
Answer: 24 plants

Question. There are 500 children in a school. For a P.T. drill they have to stand in such a manner that the number of rows is equal to number of columns. How many children would be left out in this arrangement.
Answer: 16 children

Please click the below link to access CBSE Class 8 Mathematics Worksheet - Square and Square Roots (2)