Shortcut to find the square of a number
For example i have taken two numbers 109 and 991…….the procedure is shown below……
Step 1
Subtract the nearest power of 10 from the number. So, if you are thinking about 109, the result of step 1 will be 109 – 100 = 9. If you are taking the number 991, the result will be negative. I.e. the result will be 991 – 1000 = -9.
Step 2
Add result of step 1 to the original number. So, in the first example above, the result will be 118 and for the second example the result will be 982.
Step 3
Find the square of result from step 1. So in the first and the second example, the result will be 9 * 9 = 81.
Step 4
Combine the results of step 2 and step 3 after padding enough zeroes if required. So, the answer to the fist example 109 * 109 will be 11881 and the second example 991 * 991 will be 982081
Subtract the nearest power of 10 from the number. So, if you are thinking about 109, the result of step 1 will be 109 – 100 = 9. If you are taking the number 991, the result will be negative. I.e. the result will be 991 – 1000 = -9.
Step 2
Add result of step 1 to the original number. So, in the first example above, the result will be 118 and for the second example the result will be 982.
Step 3
Find the square of result from step 1. So in the first and the second example, the result will be 9 * 9 = 81.
Step 4
Combine the results of step 2 and step 3 after padding enough zeroes if required. So, the answer to the fist example 109 * 109 will be 11881 and the second example 991 * 991 will be 982081
For numbers which are not nearer to powers of 10 then we can go for the procedure below…
For example let us take the number 73. If we have to apply this technique, then you should know the square of 27 . So, the easy way to apply this technique is to find the nearest multiple of 10 which in this case is 70. So, following step 1 we will get 73 -70 = 3. Following step 2 we will get 73 + 3 = 76. Now comes the tricky part. We have to multiply 76 with the multiple of 10 which we used as base which in this case is 7. So 76 * 7 = 532 (If you find it difficult to multiply just break it down and think 76*7 = (70*7) + (6*7) and you will get the answer as 532)
Now follow step 3. 3 * 3 = 9. And finally to step 4, we will get 5329.
so save ur calculator cell…
robert said
nice trick