User:Vikitamishra

=                                                    MATHS MAGIC =

Numbers near to 100 -
step 1: 102 can be written as 100+2
 * Let's understand this by taking an example say 102. Here the

step 2: let the square of 102 be _ _ _   _ _ filled in this.

step 3: 102= 100 + 02. so last two digit of the square of 102 will be (02)2. That is _ _ _ 0 4.

step 4: the first two digits will be 102 + 02 = 104. so 1022 = 10404

step 1: 97= 100 - 3
 * Let's consider 97

step 2 : last two digits will be (03)2 = 09.

step 3 : subtract 3 from 97 which gives 97 - 3 = 94.

step 4 : so the final answer is 972 = 9409.

Numbers ending with 5 -
step 1 : Let the square be _ _ _ _
 * Let's take an example for better understanding say 35

step 2 : Last two digits will always be 25. That is _ _ 25

step 3: Now in 35. The consecutive number of 3 is 4. so next we need to multiply 3 and 4. That is 3 x 4 = 12

step 4 : So the first two digit will be 12. finally, 352 = 1225

similarly, 952  will be 9 x 10 = 90 and 25 in the last. so 9025.

Numbers near 50 -
step 1 : 52 = 50 + 02
 * Let's take an example . say, 52 . Here the base is 50 which is 100 divided by 2.

step 2: so the last two digits will be (02)2 = 04.

step 3 : as 52 is 2 more than 50. so add 2 to 52. so the number is 54 must be divided by 2 as the base is 50 half of 100.

step 4: 52 / 2 = 27. So the first two digit is 27 and the final number is 2704.

similarly we can find square of any numbers by choosing suitable base.

Multiplication by 11
Lets take an example for better understanding. say 24 x 11.

step 1: So first and last digit will be 2 and 4

step 2 : and the middle digit will be sum of these digit. that is 2 +4 = 6

step 3 : 24 x 11 = 264.

in general the middle digits will be some of neighbor digit.