Math Shortcuts

Squaring of Two numbers

Consider a simple example 9²

Step 1: Consider the nearest base (here 10).

Step 2: As 9 has a deficiency of 1 (10 – 9 = 1), we should decrease it further by 1, and set down our LHS of the Answer as ‘8’.

Step 3: On the RHS put the square of the deficiency (here 1).

 We get 9² = 81.

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Now Consider 102

1) Base is 100

2) Deficiency is ‘-2’ (100 – 102 = -2)

  Therefore we subtract ‘-2’ from 102

102 – (-2) = 104

This is our RHS

3) Our LHS now becomes (-2)² which is 4

 Since the base is 100 we write it as ’04’, so that we get 102² = 10404

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For multiplication also we use the same technique

Consider 28²

1) Let 20 be the Working Base and 10 as the Main Base.

 Therefore x = (Main Base)/ (Working Base) = 10/20 = 1/2

2) Here the deficiency = 20 – 28 = -8

Therefore RHS = 28 – (-8 ) = 36

Divide by x i.e. by (1/2).

We get   36/ (1/2) = 72.   This is the required RHS.

3) LHS = (-8 )² = 64

Since Main Base is 10, we put only ‘4’ on the LHS and carry over ‘6’ to the RHS

Therefore we get

28² = 72+6 | 4 == 784

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Some More Examples

36² = 128 |₁ 6 = 1296                (Base = 40)

522 = 27 | 04 = 2704               (Base = 50)

9972 = 994 | 009 = 994009      (Base = 1000)

10042 = 1008 | 016 = 1008016    (Base =1000)

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