Aptitude Simplification and Formulas

March 15, 2023

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Aptitude Simplification and Formulas

Simplification is based on fundamental Math calculations and some other Algebraic themes. Simplification is less time consuming and having higher accuracy. Simplification is converting or finding the missing values from the long and complex expressions using the basic BODMAS rules.

BODMAS Rule

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

Simplification Formulas

(a + b)² = a²+ b²+ 2ab
(a – b)² = a²+ b²– 2ab
(a + b) (a – b) = a²– b²(a + b)²– (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 read:

HTML	DBMS
Data Structure	Aptitude
C Programming	Reasoning
E-LEARNING	Sangamner News

Aptitude Simplification and Formulas

Aptitude Simplification and Formulas

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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

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

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

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

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

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

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

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

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