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Maths Wiz Class 8 Solutions Chapter 3 Squares and Square Roots Cubes and Cube Roots
Welcome to NCTB Solutions. Here with this post we are going to help 8th class students for the Solutions of Maths Wiz Class 8 Math Book, Chapter 3, Squares and Square Roots Cubes and Cube Roots. Here students can easily find step by step solutions of all the problems for Squares and Square Roots Cubes and Cube Roots, Exercise 3A, 3B, 3C, 3D and 3E Also here our mathematics teacher’s are solved all the problems with easily understandable methods with proper guidance so that all the students can understand easily. Here in this post students will get chapter 3 solutions. Here in this post all the solutions are based on ICSE latest Syllabus.
Squares and Square Roots Cubes and Cube Roots Exercise 3A Solution :
Question no – (1)
Solution :
(a) 122
= 12 × 12
= 144
(b) 92
= 9 × 9
= 81
(c) 282
= 28 × 28
= 784
(d) 392
= 39 × 39
= 1521
(e) 2152
= 215 × 215
= 46225
Question no – (2)
Solution :
(a) 784
= Perfect Square
(b) 1296
= Perfect Square
(c) 7500
= Not perfect square
(d) 5184
= Perfect square
(e) 980
= Not perfect square
(f) 4050
= not perfect square
Question no – (3)
Solution :
(a) 240
∴ 240 = 4 × 4 × 3 × 5
∴ The smallest number is – 15
(b) 432
∴ 432 = 4 × 4 × 17
∴ The smallest number is 17
(c) 2592
∴ 2592 = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3
∴ The smallest number is = 2
(d) 18000
∴ 18000 = 4 × 4 × 3 × 3 × 5 × 5 × 5
∴ The smallest number is = 5
(e) 21952
∴ 21952 = 2 × 2 × 2 × 2 × 2 × 2 × 7 × 7 × 7
∴ The smallest number is = 17
Question no – (4)
Solution :
(a) 98
∴ 98 = 2 × 7 × 7
∴ The divider is 2
(b) 363
∴ 363 = 3 × 11 × 11
∴ The divider is 3
(c) 700
∴ 700 = 2 × 2 × 5 × 5 × 7
∴ The divider is 7
(d) 4400
∴ 44000 = 2 × 2 × 2 × 2 × 5 × 5 × 11
∴ The divider is 11
(e) 4374
∴ 4374 = 2 × 3 × 3 × 3 × 3 × 3 × 3 × 3
∴ The divider is = 2 × 3
= 6
Question no – (5)
Solution :
(a) 537
(b) 1042
(c) 6398
(g) 33493
These are not perfect squares because a square number cannot have 2, 3, 7 or 8 at the unit place.
(h) 960
(i) 72000
These are not perfect squares because, a whole numbers having odd number of zeros at the end cannot be a perfect square.
(c) 800
(d) 384
(e) 625
(j) 1571
May be perfect squares.
Question no – (6)
Solution :
(a) 6092
The unit digit squares = 92 = 81
(b) 3272
The unit squares = 72 = 49
(c) 3252
The unit digit square = 52 = 25
(d) 3412
The unit digit squares = 12 = 1
(e) 5462
The unit square digit square = 62 = 36
Therefore, (a) 6092 (d) 3412 would end with the digit 1.
Question no – (7)
Solution :
As per the given numbers only,
(c) 2762 have digit 6 at unit places.
Question no – (8)
Solution :
(a) 642
= The unit digit square = 42 = 16
∴ The unit digit of the squares is 6
(b) 932
= The unit digit squares = 32 = 9
∴ The unit digit of the square is 9
(c) 2062
The unit digit square = 62 = 36
∴ The unit digit of the squares is 6
(d) 1352
= The unit digit squares = 52 = 25
∴ The unit digit of the square is 5
(e) 4992
= The unit digit square = 92 = 81
∴ The unit digit of the square = 1
(f) 2382
= The unit digit square = 82 = 64
∴ The unit digit of the square 4
(g) 6072
= The unit digit square = 72 = 49
∴ The unit digit of the square 9
(h) 6522
The unit square = 22 = 4
∴ The unit digit of two square is = 4
(i) 6502
The unit digit square = 02 = 00
∴ The unit digit of the square is = 0
(j) 9712
The unit digit square =m 12 = 1
∴ The unit digit of the square is 1
Question no – (9)
Solution :
The square of odd numbers are odd numbers and the square of even numbers are even numbers.
Therefore,
(a) 517 (e) 945 (f) 719 are Odd.
(b) 234 (c) 300 (d) 718 are Even.
Question no – (10)
Solution :
(a) 40
∴ (0)2 = 00
∴ The number of zero is 2
(b) 400
(00)2 = 0000
The number of zero is 4
(c) 8000
= (000)2 = 000000
The number of zero is 6
(d) 60,000
= (0000)2 = 00000000
The number of zero is 8
Question no – (11)
Solution :
(a) 62 and 72
= Number of numbers lying between 62 and 72 are,
= 2 × 6 = 12
(b) 192 and 202
= Number of numbers lying between 192 and 202 are,
= 2 × 19 = 38
(c) 492 and 502
= Number of numbers lying between 492 and 502 are,
= 2 × 49 = 98
(d) 752 and 762
= Number of numbers lying between 752 and 762 are,
= 2 × 75 = 150
Question no – (12)
Solution :
(a) 1002 and 1012
Non –square numbers lie between 1002 and 1012 are,
= 2 × 100 = 200
(b) 2152 and 2162
Non-square numbers lie between 2152 and 2162 are,
= 2 × 215 = 430
(c) 5002 and 5012
Non-square numbers lie between 5002 and 5012 are,
= 2 × 500 = 1000
Question no – (13)
Solution :
(a) 232
= 232-1/2 + 232 + ½
= 529 –1/2 + 529 +1/2
= 528/2 + 530/2
= 264 + 265
= 529
(b) 152
= 152 – 1/2 + 152 + ½
= 224/2 + 226/2
= 112 + 113
= 225
(c) 192
= 192-1/2 + 192+1/2
= 360/2 + 362/2
= 180 + 181
= 361
(d) 252
= 252-1/2 + 252+1/2
= 624/2 + 626/2
= 312 + 313
= 625
(e) 172
= 172-1/2 + 172+1/2
= 288/2 + 280/2
= 144 + 145
= 289
Question no – (14)
Solution :
(a) 242 – 232
= 24 + 23
= 47
(b) 592 – 582
= 59 + 58
= 117
(c) 752 – 742
= 75 + 74
= 149
(d) 1022 – 1012
= 102 + 101
= 203
Question no – (15)
Solution :
(a) 1 + 3 + 5 + 7 + 9
Given addition series,
= sum of first 5 odd numbers
= 52 = 25
(b) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19
Given addition series,
= sum of first 10 odd numbers
= 102 = 100
(c) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23
Given series,
= sum of first 12 odd numbers
= 122 = 144
Question no – (16)
Solution :
(a) Given number, 169
= 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25
(b) Given number, 64
= 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15
Question no – (18)
Solution :
112 = 121
1012 = 10201
10012 = 1002001
100012 = 100020001
1000012 = 10000200001
100000012 = 100000020000001
Question no – (19)
Solution :
12 + 22 + 22 = 32
22 + 32 + 62 = 72
32 + 42 + 122 = 132
42 + 52 + 52 = 212
52 + 62 + 302 = 312
62 + 72 422 = 432
Therefore, the missing numbers are 5, 6, and 7, 42
Squares and Square Roots Cubes and Cube Roots Exercise 3B Solution :
Question no – (1)
Solution :
(a) 4 = 2 × 2
and also 4 = (-2) × (-2)
2 and (-2) are roots of 4
(b) 81 = 9 × 9
also 81 = (-9) × (-9)
9 and (-9) are roots of 81
(c) 196 = 14 × 14
also 196 = (-14) × (-14)
(-14) and 14 are roots of 196
(d) 400 = 20 × 20
also 400 = (-20) × (-20)
20 and (-20) are roots of 400
(e) 441 = 21 × 21
also 441 = (-21) × (-21)
20, (-21) are roots of 441
(f) 0.0049 = 0.07 × 0.07 also
0.0049 = (-0.07) × (-0.07)
0.07 and (-0.07) are roots of 0.0049
(g) 0.0001 = 0.01 × 0.01
also 0.0001 = (-0.01) × (-0.01)
∴ (0.01) and (-0.01) are roots of 0.0001
(h) 3 1/16 = 49/16 = 7/4 × 7/4 also
49/16 = (- 7/4) × (- 7/4)
∴ (- 7/4) and 7/4 are roots of 3 1/16
(i) 2/14 = 9/4 = 3/2 × 3/2 also
9/4 = (- 3/2) × (- 3/2)
∴ (- 3/2) and 3/2 are roots of 2 1/4
(j) 0.0289 = 0.17 × 0.17 also
0.0289 = (-0.17) × (-0.17)
∴ (-0.17) and (0.17) are roots of 0.0289
Question no – (2)
Solution :
(a) √36
= √6 × √6
= 6
(b) – √9
= √3 × 3
= -3
(c) √121
= √11 × 11
= 11
(d) – √225
= -√15 × 15
= -15
(e) √361
= √19 × 19
= 19
(f) √900
= √30 × 30
= 30
(g) √0.09
= √0.3 × 0.3
= 0.3
(h) √0.0256
= √0.16 × 0.16
= 0.16
(i) √2.25
= √1.5 × 1.5
= 1.5
(j) √4 25/36
= √169/36
= √13 × 13/6 × 6
= 13/6
Question no – (3)
Solution :
(a) x2 = 1
or, x = ± 1 ….(Solved)
(b) 12 x2 = 108
or, x2 = 108/12
or, x2 = 9
or, x = √9
= ± 3 ….(Solved)
(c) x2 – 17 = – 1
or, x2 = 17 – 1
or, x = √16
= ± 4 ….(Solved)
(d) x2 = 16/25
or, x = ± 4/5 ….(Solved)
Question no – (4)
Solution :
(a) 484
= 484 = 2 × 2 × 11 × 11
∴ √484 = 2 × 11
= 22
(b) 2500
= 2500 = 5 × 5 × 10 × 10
∴ √2500
= 5 × 10
= 50
(c) 2025
= 2025 = 5 × 5 × 3 × 3 × 3 × 3
∴ √2025
= 5 × 3 × 3
= 45
(d) 2916
= 2916 = 2 × 2 × 3 × 3 × 9 × 9
∴ √2916
= 2 × 3 × 9
= 54
(e) 2401
= 2401 = 7 × 7 × 7 × 7
∴ √2401
= √7 × 7 × 7 × 7
= 7 × 7
= 49
(f) 6084
= 6084 = 2 × 2 × 3 × 3 × 13 × 13
∴ √6084
= 2 × 3 × 13
= 78
(g) 1 184/441
= 1 184/441 = 625/441
= 5 × 5 × 5 × 5 / 3 × 7 × 3 × 7
∴ √1 184/441
= 5 × 5/3 × 7
= 25/21
(h) 0.1936
= 0.1936 = 1936/10000
= 4 × 4 × 11 × 11/100 × 100
∴ √0.1936
= 4 × 11/100
= 44/100
= 0.44
(i) 0.0576
= 0.0576 = 576/10000
= 2 × 2 × 12 × 12/100 × 100
∴ √0.0576
= 2 × 12/ 100
= 0.24
(j) 40.96
= 40.96 = 4096/100
= 4 × 4 × 4 × 4 × 4 × 4/10 × 10
∴ √40.96
= 4 × 4 × 4 / 10
= 6.4
Question no – (5)
Solution :
(a) 768
= 768 = 4 × 4 × 4 × 4 × 3
∴ To make 768 a perfect square it should be multiplied by 3
(b) 200
= 200 = 2 × 2 × 5 × 5 × 2
∴ To make 200 perfect square it should be multiplied by 2
(c) 2880
= 2880 = 4 × 4 × 2 × 2 × 3 × 3 × 5
∴ To make 2880 perfect square it should be multiplied by 5
(d) 16807
= 16807 = 7 × 7 × 7 × 7 × 7
∴ To make 16807 perfect square it should be multiplied by 7
(e) 1331
= 1331 = 11 × 11 × 11
∴ To make 1331 perfect square it should be multiplied by 11
Question no – (6)
Solution :
(a) 3125
∴ 3125 = 5 × 5 × 5 × 5 × 5
∴ The divider will be 5
(b) 1800
∴ 1800 = 3 × 3 × 10 × 10 × 2
∴ The divider will be 2
(c) 1008
∴ 1008 = 2 × 2 × 2 × 2 × 3 × 3 × 7
∴ The divider will be 7
(d) 6912
∴ 6912 = 3 × 3 × 4 × 4 × 4 × 4 × 3
∴ The divider will be 3
(e) 2925
∴ 2925 = 5 × 5 × 3 × 3 × 13
∴ The divider will be 13
Question no – (7)
Solution :
∴ LCM of 8, 15 and 20 = 120
∴ 120 = 2 × 2 × 2 × 5 × 3
The factor 30 remains unpaired
Hence, the smallest square number divisible by 8, 15, 20 is 120 × 30 = 3600
∴ The required number is 3600.
Question no – (8)
Solution :
LCM of 3, 4, 5, 6, 8
120 = 2 × 2 × 3 × 5 × 2
The factor 30 remains unpaired
Hence the least square number divisible by 3, 4, 5, 6, 8 is 120 × 30 = 3600
Therefore, the least number will be 3600
Question no – (9)
Solution :
Let the length of side of the plat = a
∴ a2 = 101 1/400
a2 = 40401/400
a = √201 × 201/20 × 20
a =
∴ Length of side = 10 1/20 m.
Therefore, the length of one side of the plot will be 10 1/20 m.
Question no – (10)
Solution :
√162 + √138 + √121
= √162 + √38 + √11 × 11
= √162 + √38 + 11
= √162 + √49
= √162 + 7
= √169
= √13 × 13
= 13
Therefore, the value will be 13.
Question no – (11)
Solution :
√3136 = 56
= √31.36 + √0.3136
= √3136/100 + √3136/10000
= √56 × 56/10 × 10 + √56 × 56/100 × 100
= 56/10 + 56/100
= 5.6 + 0.56
= 6.16
Therefore, the value will be 6.16
Squares and Square Roots Cubes and Cube Roots Exercise 3C Solution :
Question no – (1)
Solution :
(a) 484
∴ √484 = 22
(b) 841
∴ √841 = 29
(c) 1849
∴ √1849 = 43
(d) 2704
∴ √2704 = 52
(e) 4624
∴ √4624 = 68
(f) 6724
∴ √6724 = 82
(g) 7569
∴ √7569 = 87
(h) 9801
∴ √9801 = 99
Question no – (2)
Solution :
(a) 7 522/529
= 4225/529
= √4225/529
= 65/23
(b) 8 617/784
= 6889/784
= √6889/784
= 83/28
(c) 2 766/2209
= 5184/2209
= √5184/2209
= 72/47
Question no (3)
Solution :
(a) 3.24
∴ √3.24 = 1.8
(b) 6.25
∴ √6.25 = 2.5
(c) 11.56
∴ √11.56 = 3.4
(d) 16.81
∴ √16.81 = 4.1
(e) 22.09
∴ √22.09 = 4.7
(f) 0.5041
∴ √0.5041 = 0.71
(g) 0.5625
∴ √0.5625 = 0.75
(h) 0.9216
∴ √0.9216 = 0.96
Squares and Square Roots Cubes and Cube Roots Exercise 3D Solution :
Question no – (1)
Solution :
(a) 740
∴ The subtracted number 11
(b) 1535
∴ The subtracted number 9
(c) 7926
∴ The subtracted number 5
Question no – (2)
Solution :
(a) 708
We observe that 262 <708 <272
The number to be added
272 – 708
= 729 – 708 = 21
Then, 708 would become
708 + 21 = 729 and
√729 = 27
Hence, 27 must be added
(b) 1840
We observe that
42 < 1840 <432
∴ The number to be added
= 432 – 1840
= 1849 – 1840
= 9
Thus, 9 must be added
(c) 3219
We observe that
562 < 3219 < 572
∴ The number to be added,
= 572 – 3219
= 3249 – 3219
= 30
Therefore, 30 must be added.
Question no – (3)
Solution :
Total number of soldiers – 4225 since there are as many rows as the number of soldiers in a row.
∴ √3364 = 65
∴ The number of rows = 65
For your better Understanding :
Question no – (4)
Solution :
Total number of plants = 3364
Since there are as many rows as there are trees in a row.
∴ √3364 = 58
∴ The number of rows = 58
For your better understanding :
Question no – (5)
Solution :
Total number of charity- 7225
Since each member contributed as many rupees as there were number of members.
∴ √7225 = 85
∴ The number of members in the club = 85
For your better understanding :
Squares and Square Roots Cubes and Cube Roots Exercise 3E Solution :
Question no – (1)
Solution :
(a) 12
= (12)3 = 12 × 12 × 12
= 1728
So, the cube of 12 is 1728
(b) 15
= (15)3 = 15 × 15 × 15
= 3375
Thus, the cube of 15 is 3375
(c) 30
= (30)3 = 30 × 30 × 30
= 27000
Thus, the cube of 30 is 27000
(d) 200
= (200)3 = 200 ×200 × 200
= 8000000
Thus, the cube of 200 is 8000000
(e) -3/7
= (-3/7)3 = (-3/7) × (- 3/7) × (- 3/4)
= – 27/343
Thus, the cube of -3/7 is – 27/343
(f) 1 3/8
= 1 3/8 = (11/8)3
= 11 × 11 × 11/8 × 8 × 8
= 1331/512
Thus, the cube of 1 3/8 is 1331/512
(g) 0.4
= (0.4)3 = (4/10)3
= 64/1000
= 0.064
Thus, the cube of 0.4 is 0.064
(h) 0.9
= (0.9)3 = (9/10)3
= 7291/1000
= 0.729
Thus, the cube of 0.9 is 0.729
(i) 0.02
= (0.02)3 = (2/100)3
= 8/1000000
= 0.000008
Thus, the cube of 0.02 is 0.000008
(j) -2 2/9
= -2 2/9 = (-20/9)3
= (- 20/9) × (-20/9) × (-20/9)
= – 8000/729
Thus, the cube of -2 2/9 is – 8000/729
Question no – (2)
Solution :
(a) 125
∴ 125 = 5 × 5 × 5
∴ 3 √125 = 5
It is a perfect cube.
(b) 2197
∴ 2197 = 13 × 13 × 13
∴ 3√2197 = 13
It is a perfect cube.
(c) 832
∴ 832 = 2 × 2 × 2 × 2 × 2 × 2 × 13
∴ 832 is not a perfect cube.
(d) 2744
∴ 2744 = 14 × 14 × 14
∴ 3√2744 = 14 is a perfect cube
(e) 2000
∴ 2000 = 10 × 10 × 10 × 2
∴ 2000 is not a perfect cube.
Question no – (3)
Solution :
(a) 36
36 = 6 × 6
The multiplier is 6 so
36 = 6 × 6 × 6
∴ 3 √36 = 6
(b) 121
121 = 11 × 11
The multiplier is 11 so
121 = 11 × 11 × 11
∴ 3 √121 = 11
(c) 392
392 = 2 × 2 × 2 × 7 × 7
The multiplier is 7 so
392 = 2 × 2 × 2 × 7 × 7 × 7
∴ 3 √392 = 2 × 7 = 14
Question no – (4)
Solution :
(a) 54
∴ 54 = 3 × 3 × 3 × 2
The divider is 2
∴ 27 = 3 × 3 × 3
(b) 625
∴ 625 = 5 × 5 × 5 × 5
The divider is 5
∴ 125 = 5 × 5 × 5
(c) 1536
∴ 1536 = 3 × 3 × 3 × 3 × 19
The divider is = 3 × 19
(d) 7000
∴ 7000 = 10 × 10 × 10 × 7
∴ The divider is 7
Question no – (5)
Solution :
(a) 8
= 2 × 2 × 2
3√8 = 2
∴ The cube root of 8 is 2
(b) 216
= 2 × 2 × 2 × 3 × 3 × 3
∴ 3√216 = 2 × 3 = 6
∴ The cube root of 216 is 6
(c) 1728
= 4 × 4 × 4 × 3 × 3 × 3
3√1728 = 4 × 3 = 12
∴ The cube root of 1728 is 12
(d) – 4 17/27
= – (125/27)
= – (5 × 5 × 5/3 × 3 × 3)
∴ – 3√125/27 = – 5/3
∴ The cube root of -4 17/27 is -5/3
(e) 0.027
= 27/1000
= 3 × 3 × 3/10 × 10 × 10
3√0.027 = 3/10 = 0.3
∴ The cube root of 0.027 is 0.3
(f) – 0.216
= – 216/1000
= – 6 × 6 × 6/10 × 10 × 10
∴ – 3√0.216 = – 6/10 = 0.6
∴ The cube root of -0.216 is 0.6
(g) 0.001331
= 1331/1000000
= 11 × 11 × 11/100 × 100 × 100
∴ 3√0.001331 = 11/100 = 0.11
∴ The cube root of 0.001331 is 0.11
(h) 0.002744
= 2744/1000000
= 2 × 2 × 2 × 7 × 7 × 7/100 × 100 × 100
∴ 3√0.002744 = 2 × 7/100
= 14/100
= 0.14
∴ The cube root of 0.002744 is 0.14
Next Chapter Solution :
👉 Chapter 4 👈
