AP 8th Class Maths Bits Chapter 6 Square Roots and Cube Roots with Answers

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AP State Syllabus 8th Class Maths Bits 6th Lesson Square Roots and Cube Roots with Answers

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Question 1.
If a, b, c are Pythagorean triplets then which of the following is true ?
A) a² – b² = c
B) a² + b² = c²
C) b = c² – a²
D) a² > b² + c²
Answer:
B) a² + b² = c²

Question 2
Which of the following is pythagorean triplet ?
A) (1, 2, 3)
B)(4, 5, 6)
C) (3, 4, 5)
D) (5, 6, 7)
Answer:
C) (3, 4, 5)

Question 3.
Which of the following number is doesn’t lie in the units place of a square number ?
A) 1
B) 4
C) 3
D) 5
Answer:
C) 3

Question 4.
Which of the following is not a perfect square number ?
A) 121
B) 1331
C) 1024
D) 367
Answer:
D) 367

Question 5.
\(\sqrt{625}+\sqrt{441}\) =
A) 47
B) \(\sqrt{1066}\)
C) 46
D) 45
Answer:
C) 46

Question 6.
The units digit of (123456)²
A) 6
B) 3
C) 8
D) 4
Answer:
A) 6

Question 7.
111² = …………………..
A) 12341
B) 12321
C) 12312
D) 12221
Answer:
B) 12321

Question 8.
1 + 3 + 5 + 7 + 9 =
A) 9²
B) 7²
C) 5²
D) 4²
Answer:
C) 5²

Question 9.
\(\sqrt{10201}\) =
A) 1001
B) 101
C) 111
D) 121
Answer:
B) 101

Question 10.
No. of integers lie between 4² and 5²
A) 8
B) 10
C ) 9
D) 11
Answer:
A) 8

Question 11.
(121)² is a ……………… number.
A) prime
B) odd
C) even
D) none
Answer:
B) odd

Question 12.
Which of the following is a perfect cube number ?
A) 25
B) 64
C) 81
D) 100
Answer:
B) 64

Question 13.
No. of non – perfect square numbers between n² and (n + A)² are …………………
A) \(\frac{\mathrm{n}}{2}\)
B) 2n
C) n²
D) n
Answer:
B) 2n

Question 14.
If there are no common factors other than’ 1′ among a, b, c then the triplet is called a ………………….
A) Primitive
B) Secondary
C) Triplet
D) None
Answer:
A) Primitive

Question 15.
13² = ………………. + 12²
A) 10
B) 2
C) 5²
D) 10
Answer:
C) 5²

Question 16.
\(\sqrt{225}\) = ……………….
A) 12
B) 16
C) 15
D) 13
Answer:
C) 15

Question 17.
\(\sqrt{2025}\) = ………………….
A) 35
B) 45
C) 54
D) 15
Answer:
B) 45

Question 18.
The least integer should be multiplied to 6000 to become a perfect square number is ……………………
A) 19
B) 16
C) 10
D) 15
Answer:
D) 15

Question 19.
The least number should be multiplied to 720 to become a perfect square number is ………………….
A) 13
B) 9
C) 5
D) 10
Answer:
C) 5

Question 20.
…………….. should be subtracted from 4215 to become a perfect square number.
A) 119
B) 120
C) 110
D) 1
Answer:
A) 119

Question 21.
\(\sqrt{42.25}\) =
A) 7
B) 6.5
C) 8.5
D) 5.5
Answer:
B) 6.5

Question 22.
The nearest value of \(\sqrt{\mathbf{3 0 0}}\) = ………………
A) 19
B) 31
C) 17
D) 16
Answer:
C) 17

Question 23.
The side of a square is 19 units then its area is ………………… sq. units.
A) 312
B) 191
C) 163
D) 361
Answer:
D) 361

Question 24.
The area of a square is 1024 sq.units, then its side is ……………… units.
A) 32
B) 22
C) 62
D) 92
Answer:
A) 32

Question 25.
The cube of 11 is …………………..
A) 1131
B) 1331
C) 1231
D) 1431
Answer:
B) 1331

Question 26.
The perfect square and cube number of a two digited number is ………………
A) 32
B) 91
C) 16
D) 64
Answer:
D) 64

Question 27.
7 + 9 + 11 = ………………..
A) 3 ³
B) 3⁴
C) 3⁵
D) 3¹⁰
Answer:
A) 3 ³

Question 28.
\(\sqrt[3]{4913}\) = ………………….
A) 27
B) 13
C) 18
D) 17
Answer:
D) 17

Question 29.
The units digit of (1997)³
A) 10
B) 3
C) 9
D) 4
Answer:
B) 3

Question 30.
The least number should be multi¬plied to 2560 to get a perfect cube number is ………………..
A) 15
B) 40
C) 25
D) 35
Answer:
C) 25

Question 31.
\(\sqrt[3]{9261}\) = ………………
A) 13
B) 21
C) 16
D) 31
Answer:
B) 21

Question 32.
\(\sqrt[3]{x}\) = 12 ⇒ x = ……………….
A) 1728
B) 1928
C) 1314
D) 1628
Answer:
A) 1728

Question 33.
The value of \(\sqrt{97}\) is nearer to ……………….
A) 14
B) 13
C) 11
D) 10
Answer:
D) 10

Question 34.
6³ = …………………
A) 161
B) 216
C) 116
D) 117
Answer:
B) 216

Question 35.
The side of a square is 72 cm then its perimeter is ……………. cm.
A) 298
B) 148
C) 288
D) 188
Answer:
C) 288

Question 36.
How many integers are in between the squares of 25, 26 …………………..?
A) 50
B) 60
C) 70
D) 100
Answer:
A) 50

Question 37.
The units digit in the square of 431 is …………………
A) 3
B) 7
C) 0
D) 1
Answer:
D) 1

Question 38.
(2⁴)² = ………………
A) 512
B) 156
C) 258
D) 256
Answer:
D) 256

Question 39.
3⁵ = …………….
A) 243
B) 81
C) 813
D) 432
Answer:
A) 243

Question 40.
If we multiply 8788 by ……………… then we get a perfect cube.
A) 7
B) 4
C) 2
D ) 3
Answer:
C) 2

Question 41.
\(\sqrt[3]{2744}\) = ………………
A) 14
B) 24
C) 34
D) 16
Answer:
A) 14

Question 42.
\(\sqrt{175.2976}\) = ………………
A) 36.15
B) 81.14
C) 11.24
D) 13.24
Answer:
D) 13.24

Question 43.
(√a) = ………………
A) √a
B) 2a
C) \(\frac {a}{2}\)
D) a
Answer:
D) a

Question 44.
\(\sqrt{1471369}\) = ………………….
A) 1213
B) 1321
C) 1132
D) 1141
Answer:
A) 1213

Question 45.
The square root of 6084 = ……………….
A) 87
B) 78
C) 88
D) 68
Answer:
B) 78

Question 46.
√2 = ………………
A) 1.414
B) 1.5
C) 1.814
D) 1.3
Answer:
A) 1.414

Question 47.
\(\sqrt{169}+\sqrt{25}\) = ……………….
A) 18
B) 19
C) 13
D) 12
Answer:
A) 18

Question 48.
\(\sqrt{176+\sqrt{2401}}\) = …………………..
A) 25
B) 15
C) 31
D) 35
Answer:
B) 15

Question 49.
In the expansion of 3¹¹ the units digit is ……………..
A) 3
B) 7
C) 10
D) 16
Answer:
B) 7

Question 50.
Car number of Jaya is 8289 then the square root of that number is ………………
A) 32
B) 70
C) 83
D) None
Answer:
D) None

Question 51.
\(\sqrt{9025}\) = ……………….
A) 95
B) 59
C) 69
D) 73
Answer:
A) 95

Question 52.
1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 = ………………
A) 132
B) 168
C) 139
D) 169
Answer:
D) 169

Question 53.
How many cube numbers are there between 1 to 100 ?
A) 9
B) 10
C) 3
D) 13
Answer:
C) 3

Question 54.
How many digits are there in the square of 72?
A) 4 or 3
B) 3 or 6
C) 2 or 7
D) None
Answer:
A) 4 or 3

Question 55.
\(\sqrt{121}\) = …………..
A) 11
B) 16
C) 31
D) 12
Answer:
A) 11

Question 56.
3² + 4² + K², K = ……………..
A) 10
B) 13
C) 5
D) 25
Answer:
C) 5

Question 57.
How many integers are there between 9² and 10² ?
A) 16
B) 13
C) 28
D) 18
Answer:
D) 18

Question 58.
\(\sqrt{55}\) is ……………..
A) not, a square number
B) square number
C) cube number
D) value is 10
Answer:
A) not, a square number

Question 59.
\(\sqrt[3]{64}\) = ……………..
A) 9
B) 16
C) 10
D) 4
Answer:
D) 4

Question 60.
Sum of n odd number is ……………….
A) n²
B) 2n
C) n
D) n-1
Answer:
A) n²

Question 61.
Identify Pythagorean Triplet.
A) 1, 2, 7
B) 8, 9, 6
C) 3, 4, 6
D) 6, 8, 10
Answer:
D) 6, 8, 10

Question 62.
8² + K² – 17² then K = …………….
A) 15
B) 16
C) 19
D) 20
Answer:
A) 15

Question 63.
\(\sqrt{4^{4} \times 5^{4}}\) = ………………
A) 4
B) 4 × 5
C) 4² × 5²
D) 4 × 5
Answer:
C) 4² × 5²

Question 64.
\(\sqrt{\frac{25}{64}}\) = ……………..
A) \(\frac{5}{9}\)
B) \(\frac{5}{8}\)
C) \(\frac{15}{31}\)
D) \(\frac{5}{4}\)
Answer:
B) \(\frac{5}{8}\)

Question 65.
√1 = ……………
A) 0
B) 1
C) 6
D) 4
Answer:
B) 1

Question 66.
\(\sqrt{\mathbf{3 3 8 8}}\) = ……………
A) \(\sqrt[30]{7}\)
B) \(\sqrt[10]{7}\)
C) \(\sqrt[12]{7}\)
D) \(\sqrt[22]{7}\)
Answer:
D) \(\sqrt[22]{7}\)

Question 67.
\(\sqrt[3]{500} \times \sqrt[3]{686}\) = ……………….
A) 16
B) 30
C) 70
D) 80
Answer:
C) 70

Question 68.
\(\sqrt{0.4489}\) = ………………
A) 0.67
B) 6.7
C) 8.5
D) 7.7
Answer:
A) 0.67

Question 69.
\(\sqrt{12 \frac{169}{676}}\) = ……………….
A) 2\(\frac{4}{5}\)
B) 9\(\frac{3}{7}\)
C) 3\(\frac{1}{26}\)
D) 3\(\frac{13}{26}\)
Answer:
D) 3\(\frac{13}{26}\)

Question 70.
15³ = ………………….
A) 3375
B) 7375
C) 1375
D) 1525
Answer:
A) 3375

Question 71.
\(\sqrt{142884}\) =
A) 144
B) 278
C) 178
D) 378
Answer:
D) 378

Question 72.
\(\sqrt{1156}\) = x then x = ……………..
A) 44
B) 34
C) 84
D) 94
Answer:
B) 34

Question 73.
1, 4, 9, 16, 25 are ………………… numbers.
A) Square
B) Cube
C) Pure
D) None
Answer:
A) Square

Question 74.
21² = ……………….
A) 144
B) 441
C) 141
D) 191
Answer:
B) 441

Question 75.
(0.2)² = …………..
A) 0.4
B) 0.004
C) 0.45
D) 0.04
Answer:
D) 0.04

Question 76.
(-2)³ = ……………..
A) 8
B) \(\frac{1}{8}\)
C) \(\frac{1}{3^{2}}\)
D) -8
Answer:
D) -8

Question 77.
\(\sqrt[3]{\mathbf{p}}\) = 7, p = …………….
A) 416
B) 189
C) 343
D) 143
Answer:
C) 343

Question 78.
If √2 = 1.414 then the value of \(\sqrt{\frac{200}{49}}\) = ………….
A) 2.02
B) 20.2
C) 30.2
D) 21.2
Answer:
A) 2.02

Question 79.
If n³ = 2744 then the value of n² – 11 is ………….
A) 145
B) 175
C) 165
D) 185
Answer:
D) 185

Question 80.
\(\sqrt[3]{1512} \times \sqrt[3]{49000}\) = …………….
A) 160
B) 420
C) 129
D) 120
Answer:
B) 420

Question 81.
\(\sqrt{\frac{0.01}{0.81}}\) = …………….
A) \(\frac{1}{5}\)
B) \(\frac{1}{2}\)
C) \(\frac{1}{9}\)
D) 9
Answer:
C) \(\frac{1}{9}\)

Question 82.
\(\sqrt{2 \frac{14}{25}}\) = …………….
A) \(\frac{8}{7}\)
B) \(\frac{8}{5}\)
C) \(\frac{5}{8}\)
D) \(\frac{1}{3}\)
Answer:
B) \(\frac{8}{5}\)

Question 83.
\(\sqrt[3]{217}\) = …………………
A) 7
B) 8
C) 9
D) None
Answer:
D) None

Question 84.
In 1, 8, □ 64, □ = …………….
A) 27
B) 25
C) 26
D) 10
Answer:
A) 27

Question 85.
Which of the following number is called Ramanujans number ?
A) 1729
B) 1728
C) 1818
D) 1719
Answer:
A) 1729

Question 86.
\(\) = ………………
A) 0.011²
B) 0.11
C)0.11²
D) 0.11⁴
Answer:
B) 0.11

Question 87.
1³ + 2³ =
A) 10
B) 3³
C) 3²
D) 92
Answer:
C) 3²

Question 88.
\(\) = ………………
A) 0.5
B) 0.2
C) 0.7
D) 0.45
Answer:
B) 0.2

Question 89.
Identify perfect cube among the following:
A) 512
B) 14
C) 100
D) 96
Answer:
A) 512

Question 90.
\(\sqrt[3]{\frac{1}{27}}\) = ………………
A) \(\frac{1}{8}\)
B) \(\frac{1}{4}\)
C) \(\frac{1}{6}\)
D) \(\frac{1}{3}\)
Answer:
D) \(\frac{1}{3}\)

Question 91.
a + b + c = 0 then a³ + b³ + c³ = ………………
A) \(\frac{a b c}{3}\)
B) 3 abc
C) ab+c
D) \(\frac{\mathrm{ab}}{\mathrm{c}}\)
Answer:
B) 3 abc

Question 92.
12³+ 1³ = ……………….
A) 1718
B) 1719
C) 1729
D) 1829
Answer:
C) 1729

Question 93.
1³ + 2³ + 3³ = ………………
A) 5²
B) 6²
C) 8²
D) 9²
Answer:
B) 6²

Question 94.
Cube root of 2545 is ………………..
A) 10
B) 20
C) 25
D) None
Answer:
D) None

Question 95.
Kishore told “Every number is asquare number”. Krishna told “Every number is a pure number”.
In the above two statements who is correct ?
A) Kishore
B) Krishna
C) Both are correct
D) Both are false
Answer:
D) Both are false

Question 96.
Identify polyndrome number in the following numbers.
A) 15651
B) 16566
C) 15655
D) 165167
Answer:
A) 15651

Question 97.
If y = x³ then ……………….
A) x = \(\sqrt[3]{y}\)
E) x = √y
C) √x = y²
D) None
Answer:
A) x = \(\sqrt[3]{y}\)

Question 98.
\(\sqrt[3]{9261}\) = ………………..
A) 11
B) 41
C) 21
D) 14
Answer:
C) 21

Question 99.
17 < √x < 18, x = ……………….
A) 100
B) 900
C) 300
D) 20
Answer:
C) 300

Question 100.
A solid with 6 equal square faces on all the surfaces is called …………………..
A) Side
B) Cube
C) Complete cube
D) Cuboid
Answer:
B) Cube