Isn’t it great, if you can calculate faster in competitive exams or in daily life? In competitive exams you need to solve more number of problems in less time. So, people, nowadays running behind the coaching centers for shortcuts. But it is absolutely useless if you don’t have conceptual clarity. Here is the speed math rule to calculate Square of a number near to 10^x. Check other speed math rules here.
To square numbers close to the bases of powers of 10 i.e. 10, 100, 1000 and so on easily at extremely fast speed, just follow the steps below:

Step-1: Find the surplus or deficit from the base 10, 100, 1000 & so on

Step-2: Add the surplus (if it is more than base) with or subtract the deficit (if it is less than base) from the whole number given and put the result.

Step-3: Find the square of surplus or deficit and write the result in the last places. Be sure that, since 10 has 1 zero so, 1 more digit to go for numbers near 10, since 100 has 2 zeros so, 2 more digits to go for numbers near 100, accordingly since 1000 has 3 zeros, 3 more digits to go for numbers near 1000 and so on. So, carry forward or put extra zero(s) if necessary to place the digits accurate.

We use the algebraic formula

x2 = (x2 – y2) + y2 = (x + y)(x -y) + y2

Ex 1: (98)2 = (98 – 2) (98 + 2) + 22 = 9600 + 4 = 9604

Ex 2: (103)2 = (103 + 3)(103 – 3) + 32 = 10600 + 9 = 10609

Ex 3: (993)2 = (993 – 7)(993 + 7) + 72 = 986000 + 49 = 986049

Ex 4: (1008)2 = (1008 – 8)(1008 + 8) + 82 = 1016000 + 64 = 1016064

This is speed math trick 3 on square of a number near to 10^x. Please check other speed math tricks here.

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