product two consecutive odd numbers

Product of two consecutive odd numbers :

Even numbers are 1,3,5,7,9,11,13,15,17,19,21,23,25,.....

Odd  number means when we divide a number with 2,then the remainder is equal to one.

Difference between the two odd numbers is 1.

Now we will discuss the product of two odd  numbers. Now the product of two even numbers assumed to be 5x7 can be written as (6-1)x(6+1).

                             5x7= (6-1)x(6+1)

From the above we write general formula as 5x7= (6-1)x(6+1)=6²-1²  =36-1=35

Now we can observe the result as one less than the square number. So now we can observe the following table. Column 1&2 reprecent the adjacent odd numbers. Column 3 represent the product of two adjacent odd numbers. Column 4 represent  the nearest square number. This  will arrive by adding 1 to the product  of two odd  numbers.

NUMBER1	NUMBER2	PRODUCT	NEAREST SQUARE NO.
1	3	3	4
3	5	15	16
5	7	35	36
7	9	63	64
9	11	99	100
11	13	143	144
13	15	195	196
15	17	255	256
17	19	323	324
19	21	399	400
21	23	483	484
23	25	575	576
25	27	675	676
27	29	783	784
29	31	899	900
31	33	1023	1024
33	35	1155	1156
35	37	1295	1296
37	39	1443	1444
39	41	1599	1600
41	43	1763	1764
43	45	1935	1936
45	47	2115	2116
47	49	2303	2304
49	51	2499	2500
51	53	2703	2704

Now we will see how to solve the problems based on the product two consecutive even numbers.

Problem 1:product of two consecutive odd  numbers is 143. What are those numbers.

Solution: step1: product of two consecutive odd numbers is 143

                  Step2: add 1 to 143 it will become 144

                 Step3: finding the square root of 144 that is 12

                 Step4:then add 1 to 12, and subtract 1 from 12.

                 Step5: then those numbers are 11,13

Problem2:product of two consecutive odd numbers is 399. What are those numbers.

Solution: step1: product of two consecutive odd  numbers is 399

                  Step2: add 1 to 399 it will become 400

                 Step3: finding the square root of 400 that is 20

                 Step4:then add 1 to 20, and subtract 1 from 20.

                 Step5: then those numbers  are 19,21

Problem 3:product of two consecutive odd numbers is 255. What are those numbers.

Solution: step1: product of two consecutive odd numbers is 255

                  Step2: add 1 to 255 it will become 256

                 Step3: finding the square root of 256  that is 16

                 Step4:then add 1 to 16, and subtract 1 from 16.

                 Step5: then those numbers are 15,17

Problem 4:product of two consecutive odd numbers is 783. What are those numbers.

Solution: step1: product of two consecutive odd  numbers is 783

                  Step2: add 1 to 783 it will become 784

                 Step3: finding the square root of 784 that is 28

                 Step4:then add 1 to 28, and subtract 1 from 28.

                 Step5: then those numbers are 27,29