CBSE Class 8 Mathematics Squares and Square Roots MCQs

Question. The square root of 441/961 is
(A) 21/39
(B) 37/21
(C) 21/31
(D) 11/13

Answer: C

Question. If M is a square number, then the next immediate square number is
(A) M + 5
(B) M + 2√M + 1
(C) M2 + 2M
(D) none of these

Answer: B

Question. √1/16 + 1/9 =
(A) 7/12
(B) 25/144
(C) 5/12
(D) none

Answer: C

Question. If √1+27/169 = 1+x/13 then x =
(A) 1
(B) 14
(C) cannot be determined
(D) none of these

Answer: A

Question. The square root of 71 × 72 × 73 × 74 + 1 is
(A) 9375
(B) 9625
(C) 5625
(D) 5255

Answer: D

Question. If a square number ends in 6, the preceding figure is
(A) an even number
(B) an odd number
(C) a prime number
(D) a composite number

Answer: B

Question. The value of √(-1)√(-1) is
(A) – 1
(B) + 1
(C) ± 2
(D) none

Answer: A

Question. The value of (501)² – (500)² is
(A) 1
(B) 101
(C) 1001
(D) none of these

Answer: C

Question. Which of the following is a Pythagorean triplet?
(A) (6, 8, 10)
(B) (3, 4, 7)
(C) (5, 12, 18)
(D) none of these

Answer: A

Question. The value of 1 + 3 + 5 + 7 + 9 + ..... + 25 is
(A) 196
(B) 625
(C) 225
(D) 169

Answer: D

Question. The smaller number by which 396 must be multiplied so that the product becomes a perfect square is
(A) 5
(B) 11
(C) 3
(D) 2

Answer: B

Question. The value of √99 × √396 is
(A) 208
(B) 198
(C) 254
(D) none of these

Answer: B

Question. Square root of 0.081/0.0064 x 0.484/6.25 x 2.5/21.1 is
(A) 0.45
(B) 0.75
(C) 0.95
(D) 0.75

Answer: A

Question. √1+ √1+ √1+ .........
(A) equals 1
(B) lies between 0 and 1
(C) lies between 1 and 2
(D) is grater than 2

Answer: C

Question. The value of 1+√0.01/1-√0.1 is close to
(A) 0.6
(B) 1.1
(C) 1.6
(D) 1.7

Answer: C

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

Answer: D

Question. Evaluate √41- √21- √19 - √9
(A) 3
(B) 6
(C) 5
(D) 6.4

Answer: B

Question. A number added to its square gives 56. The number is
(A) 12
(B) 9
(C) 8
(D) 7

Answer: D

Question. The least number which must be subtracted from 6156 to make its perfect square is
(A) 62
(B) 72
(C) 52
(D) 82

Answer: B

Question. 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) 1636
(C) 3664
(D) 6481

Answer: A

Question. The square of a natural number subtracted from its cube is 48. The number is
(A) 6
(B) 5
(C) 4
(D) 8

Answer: C

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

Answer: A

Question. If √16/49 = x/49 then x =
(A) 4
(B) 7
(C) 16
(D) 28

Answer: D

Question. The square root of a perfect square containing ‘n’ digits has ________ digits.
(A) n+1/2
(B) n/2
(C) A or B
(D) none

Answer: C

Question. The area of a square field is 80,244/729 sq. m. The length of each side of the field is
(A) 8.96 m
(B) 10.26 m
(C) 13.54 m
(D) none

Answer: A

Question. The square root of 1764 is
(A) 32
(B) 42
(C) 48
(D) 38

Answer: B

Question. The square root of 53361 is
(A) 231
(B) 211
(C) 261
(D) 249

Answer: A

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

Answer: A

Question. The square root of 390625 is
(A) 645
(B) 225
(C) 735
(D) 625

Answer: D

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

Answer: B

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

Answer: C

Question. The least number of 4 digits which is a perfect square is
(A) 1000
(B) 1004
(C) 1016
(D) 1024

Answer: D

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

Answer: B

Question. The value of √0.9 is (approx)
(A) 0.3
(B) 0.6
(C) 0.9
(D) 0.4

Answer: C

Question. 

Answer: A

Question. Which of the following numbers, where in some of the digits have been suppressed by symbols, can possibly be the perfect square of a 3 digit odd number?
(A) 65 × × × 1
(B) 9 × × 1
(C) 10 × × × 4
(D) 9 × × × × × 5

Answer: A

Question. The least number which must be added to 196201 to make it a perfect square is
(A) 42
(B) 44
(C) 48
(D) 50

Answer: B

Question. The least number which must be subtracted from 2509 to make it a perfect square, is
(A) 6
(B) 9
(C) 12
(D) 14

Answer: B

Question. The least number of numbers to be deleted from the set {1, 2, 3,....13, 14, 15} so that the product of the remaining numbers is a perfect square is
(A) 1
(B) 2
(C) 3
(D) 4

Answer: C

Question. A gardener has 1000 plants. The minimum number of plants he needs more to plant these in such a way that the number of rows and the number of columns remain same is
(A) 100
(B) 24
(C) 89
(D) 156

Answer: B

Question. If the diagonal of a square is doubled, the area of the square becomes
(A) 2 times
(B) 3 times
(C) 4 times
(D) 6 times

Answer: C

Question. The students of class 8 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. The number of students in the class, is
(A) 47
(B) 48
(C) 49
(D) 50

Answer: C

Question. The smallest number by which 252 must be multiplied so that the product is a perfect square is
(A) 7
(B) 6
(C) 5
(D) 12

Answer: A

Question. The value of √900 + √0.09 + √0.000009 is
(A) 30.003
(B) 30.330
(C) 30.303
(D) 30.333

Answer: C

Question. If √2√2√2√2√2 = x , then x is
(A) 0
(B) 1
(C) 2
(D) 2^31/32

Answer: D

Question. The number must be subtracted from 16161 to get a perfect square is
(A) 31
(B) 32
(C) 33
(D) 34

Answer: B

Question. √284 + √52 + √144
(A) 14
(B) 16
(C) 16.6
(D) 18.8

Answer: B

Question. The smallest square number which is divisible by each of the number 6, 9 and 15, is
(A) 100
(B) 400
(C) 900
(D) 1024

Answer: C

Question. The smallest number by which 180 must be multiplied so that it becomes a perfect square is
(A) 6
(B) 9
(C) 3
(D) 5

Answer: D

Question. The lest square number, which is exactly divisible by each one of the numbers 12, 15, 18 is
(A) 3844
(B) 3364
(C) 3721
(D) 3600

Answer: D

Question. The square root of 7 correct upto two places of decimal is
(A) 2.64
(B) 2.65
(C) 2.66
(D) 2.67

Answer: B

Question. Between which two consecutive whole numbers does √95 lie?
(A) 7 and 8
(B) 8 and 9
(C) 9 and 10
(D) 10 and 11

Answer: C

Question. If √(12+√12+√12+......) = x , then the value of x is
(A) 3
(B) 4
(C) 6
(D) greater than 6

Answer: B

Question. If √3 = 1.732 and √2 = 1.414, then the value of 1/√3+√2 is
(A) 0.064
(B) 0.308
(C) 0.318
(D) 2.146

Answer: C

Question. Largest perfect square number of three digits divisible by 10, 15 and 25 is
(A) 625
(B) 999
(C) 900
(D) 1024

Answer: C

Question. The least square number exactly divisible by each one of the numbers 8, 12, 15, 20 is
(A) 3652
(B) 3600
(C) 4900
(D) 1500

Answer: B

Question. The greatest six-digit number, which is a perfect square is
(A) 998001
(B) 995001
(C) 997001
(D) 996001

Answer: A

Question. A decimal fraction is multiplied by itself. If the product is 176.252176. The fraction is
(A) 13276
(B) 13.267
(C) 13.287
(D) 13278

Answer: A

Question. If √2401 = √7^x , then the value of x is
(A) 3
(B) 4
(C) 5
(D) 6

Answer: B

Question. The smallest number by which 9408 must be divided so that the quotient is a perfect square, is
(A) 2
(B) 3
(C) 5
(D) 7

Answer: B

Question. The square root of the quotient which is a perfect square obtained when 9408 is divided by smallest number is
(A) 56
(B) 168
(C) 54
(D) 55

Answer: A

Question. If √2 + √x = √3 , then x =
(A) 1
(B) √7
(C) 7
(D) 49

Answer: D

Question. If √.05x5x a =.5x.05x √b , then a/b = ?
(A) 0.0025
(B) 0.025
(C) 0.25
(D) 2.5

Answer: B

Question. If √0.01+ √0.0064 = x , then the value of x is
(A) 0.3
(B) 0.03
(C) √0.18
(D) none of these

Answer: A

Question. The value of x, for which ax² – c = 0 

Answer: A

Question. If value of √15625 =125, then the value of √156.25 + √1.5625 is
(A) 137.5
(B) 1.375
(C) 13.75
(D) 0.1375

Answer: C

Question. Consider the following statements
1. √(√5-2)² = √5-2
2. √(√6-√7)² = √7-√6. Of these statements
(A) 1 alone is correct
(B) 2 alone is correct
(C) both 1 and 2 are false
(D) both 1 and 2 are correct

Answer: D

Question. Square numbers can only have......at the end
(A) Odd number of zeros
(B) Even number of zeros
(C) Both (A) and (B)
(D) none of these

Answer: B

Question. The least perfect square number divisible by 3, 4, 5, 6, 8 is
(A) 900
(B) 1200
(C) 2500
(D) 3600

Answer: D

Question. The value of √99 x √396 is
(A) 208
(B) 198
(C) 254
(D) 205

Answer: B

Question. If x = √3018 +√36 +√169 , the value of x is
(A) 55
(B) 44
(C) 63
(D) 42

Answer: A

Question. If √0.9x0.09x x = 0.9x0.09x √z , then the value of
(A) 0.081
(B) 0.810
(C) 081
(D) 8.09

Answer: A

Question. If √169/x = 1.30 then the value of x is
(A) 100
(B) 1000
(C) 10
(D) 1000

Answer: A

Question. The value of √7+2√10 is
(A) √6 + v1
(B) √4 + √3
(C) √5 + √2
(D) 2 + √5

Answer: C

Question. 

Answer: B

Question. A number is 64 times the square of its reciprocal. The number is
(A) 10
(B) 4
(C) 2
(D) 16

Answer: B

Question. The smallest perfect square number exactly divisible by 4, 5, 6, 15, 18 is
(A) 800
(B) 225
(C) 361
(D) 900

Answer: D

Question. A gardener plants 17956 trees in such a way that there are as many rows as there are trees in a row.
The number of trees in a row are
(A) 136
(B) 164
(C) 134
(D) 166

Answer: C

1. The square of a number is that number raised to the power 2.

2. A natural number is called a perfect square if it is the square of some natural number.

3. Properties of Squares
(a) A number ending in 2, 3, 7 (or) 8 is never a perfect square.
(B) A number ending in an odd number of zeros is never a perfect square.
(C) Squares of even numbers are given
(D) Squares of odd numbers are odd.
(e) For every natural number ‘n’, we have (n + 1)² – n² = (n + 1) + n e.g., – 92 – 82 = 9 + 8 = 17.
(f) A triplet (a, b, c) of three natural numbers a, b and c is called a Pythagorean triplet if a² + b² = c².

4. The square root of a number x is that number which when multiplied by itself gives x as the product.
We denote the square root of x by √x.

5. For any positive numbers ‘a’ and ‘b’ we have
(i) √ab = √a × √b
(ii) √a/b = √a/√b.