Aptitude_Simplification

BODMAS Rule

B = Bracket
o = Of
D = Divide
M = Multiplication
A = Addition
S = Subtraction

Simplification Formulas

(a + b)2 = a+ b+ 2ab
(a – b)2 = a+ b– 2ab
(a + b) (a – b) = a– b2
(a + b)– (a – b)2 = 4ab
(a + b)2 + (a – b)2 = 2(a2 + b2)
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ac)
(a3 + b3) = (a + b)(a2 – ab + b2)
(a3 – b3) = (a – b)(a2 + ab + b2)
(a + b)3 = a3 + b3 + 3ab(a  + b)
(a – b)3  = a3 – b3 – 3ab(a – b)
(a3 + b3 + c3 – 3abc) = (a + b + c) (a2 + b2 + c2 – (ab + bc + ca)
If a + b + c = 0, then a3 + b3 +c3 = 3abc

Square, Cube, Square root and Cubic root of numbers from 1 to 50

Number Square Cube Square Root Cubic Root
1 1 1 1.000 1.000
2 4 8 1.414 1.260
3 9 27 1.732 1.442
4 16 64 2.000 1.587
5 25 125 2.236 1.710
6 36 216 2.449 1.817
7 49 343 2.646 1.913
8 64 512 2.828 2.000
9 81 729 3.000 2.080
10 100 1000 3.162 2.154
11 121 1331 3.317 2.224
12 144 1728 3.464 2.289
13 169 2197 3.606 2.351
14 196 2744 3.742 2.410
15 225 3375 3.873 2.466
16 256 4096 4.000 2.520
17 289 4913 4.123 2.571
18 324 5832 4.243 2.621
19 361 6859 4.359 2.668
20 400 8000 4.472 2.714
21 441 9261 4.583 2.759
22 484 10648 4.690 2.802
23 529 12167 4.796 2.844
24 576 13824 4.899 2.884
25 625 15625 5.000 2.924
26 676 17576 5.099 2.962
27 729 19683 5.196 3.000
28 784 21952 5.292 3.037
29 841 24389 5.385 3.072
30 900 27000 5.477 3.107
31 961 29791 5.568 3.141
32 1024 32768 5.657 3.175
33 1089 35937 5.745 3.208
34 1156 39304 5.831 3.240
35 1225 42875 5.916 3.271
36 1296 46656 6.000 3.302
37 1369 50653 6.083 3.332
38 1444 54872 6.164 3.362
39 1521 59319 6.245 3.391
40 1600 64000 6.325 3.420
41 1681 68921 6.403 3.448
42 1764 74088 6.481 3.476
43 1849 79507 6.557 3.503
44 1936 85184 6.633 3.530
45 2025 91125 6.708 3.557
46 2116 97336 6.782 3.583
47 2209 103823 6.856 3.609
48 2304 110592 6.928 3.634
49 2401 117649 7.000 3.659
50 2500 125000 7.071 3.684


Multiplication Table from 2 to 10

2 3 4 5 6 7 8 9 10
4 6 8 10 12 14 16 18 20
6 9 12 15 18 21 24 27 30
8 12 16 20 24 28 32 36 40
10 15 20 25 30 35 40 45 50
12 18 24 30 36 42 48 54 60
14 21 28 35 42 47 56 63 70
16 24 32 40 48 54 64 72 80
18 27 36 45 54 63 72 81 90
20 30 40 50 60 70 80 90 100

Multiplication Table from 11 to 20

11 12 13 14 15 16 17 18 19 20
22 24 26 28 30 32 34 36 38 40
33 36 39 42 45 48 51 54 57 60
44 48 52 56 60 64 68 72 76 80
55 60 65 70 75 80 85 90 95 100
66 72 78 84 90 96 102 108 114 120
77 84 91 98 105 112 119 126 133 140
88 96 104 112 120 128 136 144 152 160
99 108 117 126 135 144 153 162 171 180
110 120 130 140 150 160 170 180 190 200

Multiplication Table from 21 to 30

21 22 23 24 25 26 27 28 29 30
42 44 46 48 50 52 54 56 58 60
63 66 69 72 75 78 81 84 87 90
84 88 92 96 100 104 108 112 116 120
105 110 115 120 125 130 135 140 145 150
126 132 138 144 150 156 162 168 174 180
147 154 161 168 175 182 189 196 203 210
168 176 184 192 200 208 216 224 232 240
189 198 207 216 225 234 243 252 261 270
210 220 230 240 250 260 270 280 290 300

also see

C Programming language
Go Programming language
Linked List Array
Stack Queue
DBMS Reasoning
Aptitude HTML
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