Magical Calculations
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The following are the easy methods for finding the squares of two digit numbers :-

65² = 65 × 65
But you need not multiply 65 by 65 to get 65² . Use the following easy method to find the square of any two digit number ending with 5.5 is the unit digit and 6 is the ten digit in the given number 65.

To find 65² :-

Add 1 to 6 that gives you 6 + 1 = 7.
Multipy 6 by 7 :- 6 × 7 = 42.
Put 25 by the right side of 42 to give 4225 therefore 65² = 4225.

To find 85² :-

Multipy 8 by its next number 9. ie. 8 × 9 = 72
Put 25 by the side of 72 to give 7225 therefor 85² = 7225

It may be regarded as follows .
65² = (6 × 7) 100 + 25 = 4225
85² = (8 × 9) 10 0+ 25 = 7225

It may also be regarded as follows,
65² = (6² + 6) 100 + 25 = 4225
85² = (8² + 8) 100 + 25 = 7225
No steps need be shown.Only the correct answer is to be given.
46² = 46& times; 46

To find the square of any two digit number. you need not multiply 46 by 46 . You need not write any steps.
Give only the correct answer by the following easy method.
Square the unit digit in mind, 6² = 36.
put the 6 as the last digit and keep 3 in your mind. 6
multiply 4 by 6 in your mind.Double the prouduct.
Thus 4 × 6 = 24
24 × 2 =48
Add the 3 in your mind to 48 to give 48 + 3 = 51.
Put 1 on the left side of 6 and keep 5 in your mind. 16

Square the ten digit in your mind.
4² = 16

Add 5 in your mind to give 16 + 5 = 21
Put this by the left of 16 already written.
The correct answer = 2116 is obtained. 2116

Example :-

To find 78²

8² = 64 4
8 &tomes; 7 = 56
56 × 2 = 112
112 + 6 = 118 84
7² = 49
49 + 11 = 60
= 60484