Example 1: Consider 78 * 78
The product is 6084
Now look at the number 4964 - First two digits is 7*7 and last 2 digits is 8*8
4964 + 1120 would give us 6084 which is 78*78
Why 1120 - 1120 is nothing but 7*8 (of 78) multiplied by 20
Example 2: 63 * 63
The product is 3969
Now look at the number 3609 - First two digits is 6*6 and last 2 digits is 3*3
3609 + 360 would give us 3969 which is 63*63
Why 360 - 360 is nothing but 6*3 (of 63) multiplied by 20
The product is 6084
Now look at the number 4964 - First two digits is 7*7 and last 2 digits is 8*8
4964 + 1120 would give us 6084 which is 78*78
Why 1120 - 1120 is nothing but 7*8 (of 78) multiplied by 20
Example 2: 63 * 63
The product is 3969
Now look at the number 3609 - First two digits is 6*6 and last 2 digits is 3*3
3609 + 360 would give us 3969 which is 63*63
Why 360 - 360 is nothing but 6*3 (of 63) multiplied by 20
This works as per the formula - (10a + b)squared = 100asquared = bsquared + 20ab
ReplyDelete78 * 78 is (10a + b)squared
4964 is 100asquared + bsquared
1120 is 20ab