Chapter 3 : Square- Square roots and Cube-cube roots

1: Which of the following is the square of an odd number?
(a) 256              (b) 361           (c) 144              (d) 400
Ans : (b).
2: Which of the following will have 1 at its units place?
(a) 19²             (b) 17²           (c) 18²             (d) 16²
 Ans: (a).
3: How many natural numbers lie between18² and 19² ?
(a) 30             (b) 37             (c) 35               (d) 36
Ans: (d).

4:Which of the following is not a perfect square?
(a) 361              (b) 1156            (c) 1128            (d) 1681
Ans: (c).
5:  A perfect square can never have the following digit at ones place.
(a) 1         (b) 6           (c) 5               (d) 3
Ans: (d).
6:  The value of  176+2401 is
(a) 14          (b) 15         (c) 16          (d) 17
Ans: (b).
( Hints: 176+2401=176+49=225=15 )
7: Given that  5625=75 , the value of 0.5625+56.25 is:
 (a) 82.5            (b) 0.75         (c) 8.25            (d) 75.05
Ans : (c).
 [ Hints: 5625=75 , then 0.5625 = 0.75 and 56.25 = 7.5   ]

8.196 is the square of
(a) 11            (b) 12            (c) 14          (d) 16
9.Which of the following is a square of an even number?
(a) 144          (b) 169         (c) 441            (d) 625
10. A number ending in 9 will have the units place of its square as
(a) 3           (b)  9            (c) 1              (d) 6

11. Which of the following will have 4 at the units place?
(a) 14²            (b) 62²              (c) 27²             (d) 35²
12. How many natural numbers lie between 5² and 6² ?
(a) 9           (b) 10              (c) 11              (d) 12
6.Which of the following cannot be a perfect square?
(a) 841          (b) 529             (c) 198               (d) All of the above
7.The one’s digit of the cube of 23 is
(a) 6          (b) 7             (c) 3             (d)  9
8. A square board has an area of 144 square units. How long is each side of the board?
(a) 11 units          (b) 12 units             (c) 13 units                (d) 14 units
9.Which letter best represents the location of 25 on a number line?
(a)A        (b) B               (c) C                      (d)  D

Figure

10.If one member of a pythagorean triplet is 2m, then the other two members are
(a)  m, m²+1
(b)  m²+1 , m²–1

(c)  m² , m²–1

(d)  m², m+1
11.The sum of successive odd numbers 1, 3, 5, 7, 9, 11, 13 and 15 is
(a) 81          (b) 64               (c) 49              (d) 36
12.The sum of first n odd natural numbers is
(a) 2n+1      (b) n²        (c) n²–1         (d)  n²+1
13.Which of the following numbers is a perfect cube?
(a)243               (b)216              (c)392               (d)8640
14.The hypotenuse of a right triangle with its legs of lengths 3x × 4x is
   (a) 5x                      (b) 7x                     (c) 16x              (d) 25x
15.The next two numbers in the number pattern 1, 4, 9, 16, 25 ... are
(a)35, 48           (b)36, 49        (c)36, 48         (d)35,49

16.Which among 43², 67², 52², 59² would end with digit 1?
(a)43²                 (b)67²              (c)52²         (d)59²
17.A perfect square can never have the following digit in its ones place.
(a)1              (b)8           (c)0             (d)6
18.Which of the following numbers is not a perfect cube?
(a)216             (b)567             (c)125            (d)343
19. 31000 is equal to
(a)10         (b)100       (c)1       (d)None of these
20.If m is the square of a natural number n, then n is
(a)the square of m
(b)greater than m
(c)equal to m
(d)m

21.A perfect square number having n digits where n is even will have square root with
(a) n+1 digit         (b) 2n digit           (c) 3n digit           (d)  n+12 digit
22.If m is the cube root of n, then n is
(a) m³       (b) m        (c) m3        (d) 3m 

23. The value of 248+52+144 is
(a) 14           (b) 12              (c) 16              (d) 13
24.Given that 4096 = 64, the value of 4096 + 40.96 is
(a) 74           (b) 60.4             (c) 64.4          (d) 70.4

    Fill in the blanks :
25.There are _________ perfect squares between 1 and 100.
26.There are _________ perfect cubes between 1 and 1000.
27.The units digit in the square of 1294 is _________.

28.The square of 500 will have _________ zeroes.
29.There are _________ natural numbers between n² and (n + 1)²
30.The square root of 24025 will have _________ digits.
31.The square of 5.5 is _________.
32.The square root of 5.3 × 5.3 is _________.
33.The cube of 100 will have _________ zeroes.
34.1m² = _________ cm².
35.1m³ = _________ cm³.
36.Ones digit in the cube of 38 is _________.
37.The square of 0.7 is _________.
38.The sum of first six odd natural numbers is _________.
39.The digit at the ones place of 57² is _________.
40.The sides of a right triangle whose hypotenuse is 17cm are _________and _________.
41.    1.96= _________.
42.(1.2)³= _________.

43.The cube of an odd number is always an _________ number.
44.The cube root of a number x is denoted by _________.
45.The least number by which 125 be multiplied to make it a perfect square is _____________.
46.The least number by which 72 be multiplied to make it a perfect cube is _____________.
47.The least number by which 72 be divided to make it a perfect cube is _____________.
48.Cube of a number ending in 7 will end in the digit _______________.

49.  682 will have __________ at the units place.
Solution:4
50. The positive square root of a number x is denoted by __________.
Ans: x
51:The least number to be multiplied with 9 to make it a perfect cube is _______________.
Ans: 3

52: The cube of 0.3 is ____________.
Ans:  0.027

53: There are __________ perfect squares between 1 and 50.
Ans:  6
54 : The cube of 100 will have __________ zeroes.
Ans:  6
55: The square of 6.1 is ____________.
Ans:  37.21

56:The cube of 0.3 is ____________.
Ans :  0.027

57:  68² will have __________ at the units place.
Ans :   4
58: The positive square root of a number x is denoted by __________.

Ans:   x 

59: The least number to be multiplied with 9 to make it a perfect cube is _______________.
Ans:   3