Isn’t it great if you are able to calculate faster in a competitive exam or in your everyday life? In a competitive exam, you have to solve a large number of questions in a short period of time. Nowadays, people are rushing to the coaching centers for shortcuts. However, it is all for nothing if you do not have a good conceptual understanding. Here is a quicker math rule for calculating the Square of a given number near 10^x.
Check other quicker 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 onStep-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 quicker math trick 3 on square of a number near to 10^x. Please check other speed math tricks here.
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