S.chand books class 8 maths solution chapter cube and cube roots

CUBE AND CUBE ROOTS

EXERCISE 4 (A)

 

1.Write (T) for True or (F) for false:

(i) The cube root of 8000 is 200.

(ii) Each prime factor appears 3 times in its cube.

(iii) ​\( \sqrt[3]{27+64}=\sqrt[3]{27}+\sqrt[3]{64} \)

(iv) For an integer a, ​\( a^3 \)​ is always greater than ​\( a^2 \)​.

(v) The least number by which 72 must be divided to make it a perfect cube is 9.

2.Find the cubes of the following numbers.

(i) 8

(ii) ​\( -15 \)

(iii) 600

3.

(i) ​ ​\( \dfrac{5}{6} \)

(ii) \( \dfrac{-7}{9} \) 

(iii) ​\( 1\dfrac{3}{5} \)

4.

(i) 0.03

(ii) 1.7

(iii) ​\( -0.008 \)

5.Which of the following numbers are perfect cubes?

65, 128, 243, 512, 900, 1728, 4096

6.Find the cube root of the following numbers by prime factorization method.

(i) 5832

(ii) 91125

(iii) ​\( -9261 \)

(iv) ​\( \dfrac{125}{343} \)

(v) ​\( -\dfrac{2744}{4096} \)

(vi) ​\( -5\dfrac{104}{125} \)

7.Evaluate:

(i) ​\( \sqrt[3]{1.331} \)

(ii) ​\( \sqrt[3]{0.003375} \)

8.What is the smallest number by which each of the following numbers must be multiplied so that the product is a perfect cube.Also, find cube root of the product.

(i) 1125

(ii) 6912

(iii) 47916

9.Find the smallest number by which each of the following numbers must be divided so that quotient is a perfect cube. Also, find the cube root of the product.

(i) 3584

(ii) 1458

(iii) 120393

10.Find the value of :

(i) ​\( \sqrt[3]{27}+\sqrt[3]{0.008}+\sqrt[3]{0.064} \)

(ii) ​\( \bigg\{(5^2+\sqrt{10^2})\bigg\}^3 \)

(iii) ​\( \sqrt[3]{686}\times\sqrt[3]{500} \)

 

EXERCISE 4 (B)

 

Number Cube Cube Root
1 1 1.000
2 8 1.260
3 27 1.442
4 64 1.587
5 125 1.710
6 216 1.817
7 343 1.913
8 512 2.000
9 729 2.080
10 1000 2.154
11 1331 2.224
12 1728 2.289
13 2197 2.351
14 2744 2.410
15 3375 2.466
16 4096 2.520
17 4913 2.571
18 5832 2.621
19 6859 2.668
20 8000 2.714
21 9261 2.759
22 10648 2.802
23 12167 2.844
24 13824 2.884
25 15625 2.924
26 17576 2.962
27 19683 3.000
28 21952 3.037
29 24389 3.072
30 27000 3.107
31 29791 3.141
32 32768 3.175
33 35937 3.208
34 39304 3.240
35 42875 3.271
36 46656 3.302
37 50653 3.332
38 54872 3.362
39 59319 3.391
40 64000 3.420
41 68921 3.448
42 74088 3.476
43 79507 3.503
44 85184 3.530
45 91125 3.557
46 97336 3.583
47 103823 3.609
48 110592 3.634
49 117649 3.659
50 125000 3.684
51 132651 3.708
52 140608 3.733
53 148877 3.756
54 157464 3.780
55 166375 3.803
56 175616 3.826
57 185193 3.849
58 195112 3.871
59 205379 3.893
60 216000 3.915
61 226981 3.936
62 238328 3.958
63 250047 3.979
64 262144 4.000
65 274625 4.021
66 287496 4.041
67 300763 4.062
68 314432 4.082
69 328509 4.102
70 343000 4.121
71 357911 4.141
72 373248 4.160
73 389017 4.179
74 405224 4.198
75 421875 4.217
76 438976 4.236
77 456533 4.254
78 474552 4.273
79 493039 4.291
80 512000 4.309
81 531441 4.327
82 551368 4.344
83 571787 4.362
84 592704 4.380
85 614125 4.397
86 636056 4.414
87 658503 4.431
88 681472 4.448
89 704969 4.465
90 729000 4.481
91 753571 4.498
92 778688 4.514
93 804357 4.531
94 830584 4.547
95 857375 4.563
96 884736 4.579
97 912673 4.595
98 941192 4.610
99 970299 4.626
100 1000000 4.642

 1.Find the cube roots of the following numbers using table.

(i) 28

(ii) 61

(iii) 83

(iv) 350

(v) 570

(vi) 960

(vii) 4.3

(viii) 6600

(ix) 9.4

(x) 6.9

2.Find the cube roots of

(i) 76.25

(ii) 37.62

(iii) 458

(iv) 732

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