Making Your Math Simple Part III - Squaring Two Numbers Having '5' as Last Digit Just in 2 Seconds

Square of two numbers having 5 as last digit

Multiplying two similar numbers having 5 as the right most digit is very simple.

Example 1

85 x 85

Of ‘8’ and ‘5’, multiply 5 with 5 getting 25 Ans 25

Now multiply remaining number (i.e. 8) with next higher number i.e. 9. So 9 x 8 = 72 Ans 72

The answer is 7225

Example 2

65 x 65

Step 1 Multiply 5 with 5 i.e. 5 x 5 =25

Step 2 Multiply 6 with next higher number i.e. 7 , So it becomes 7 x 6 =42

Ans = 4225.

Example 3

35 x 35

Step 1

5 x 5 = 25

Step 2

4 x 3 = 12

Ans = 1225

Example 4

125 x 125

Step 1 : 5 x 5 = 25

Step 2 : 13x12 = 156

Ans = 15625

Example 5

75 x 75

Step 1 : 5 x 5 =25 Step 2 : 8 x 7=56 Ans = 5625

This formula also holds good when we multiply two number having first digit/s same and total of last digits is 10.

Let me make the things clear

27x23, 48x42, 89x81, 76x74, 127x123

Here in all the five cases the first digit is same and total of 2nd digits in every case is 10.

e.g. in 27x23, first digit of both ‘27’ and ‘23’ is same i.e. ‘2’, and total of 2nd digits is 10 (7+3=10)

The multiplication in such cases is simple

i.e. multiply the last two digits and multiply the first digit with next higher number and the problem is solved

Take for example 27x23

Step 1 : multiply ‘7 of 27’with ‘3 of 23’ i.e. 7x3=21 Ans

Step 2 : multiply 2 with next higher number i.e. 3 i.e. 3x2=6 Ans

So answer for 27x23 is 621.

Similarly

48x42 Multiply last digits i.e. 8x2=16

multiply first digit (4) with next higher number (5)=20

The answer is 2016.

In the same way

89x81 : 9x1=09 and 8x9=72 Ans is 7209 76x74 : 6x4=24 and 7x8=56 Ans is 5624 127x123 7x3=21 and 12x13=156 Ans is 15621

For more such tricks and tactics to make your math simpler, please logon to http://www.magicwithmath.com Rajinder Goswami