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sagar2911
Joined: 08 Sep 2012
Last visit: 17 Aug 2019
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Location: India
Concentration: Social Entrepreneurship, General Management
Schools: HBS '18 Stanford '18 Wharton '18 Yale '18 ISB '17
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08 Nov 2015, 08:43
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Hi All,
I happened to discover (only if someone else hasn't shared this before
) a faster way of calculating squares of any number not ending in 0 or 5.
Things you need to know: Shortcut to calculate squares of numbers ending in 5 (given at the end of post)
Suppose you have to calculate 13x13
Step1: Either choose the nearest number ending in 5, i.e. 15 or nearest number ending in 0, i.e. 10.
Let us suppose we choose 15
Step2: Square this number - 15x15
Use the shortcut to find squares ending in 5. You will get 225.
Step 3: Crucial step:
Now, since 13 is smaller than 15, you will subtract from 225 two numbers calculated as follows (Do the reverse, i.e. add when the number is bigger)
a) 13X 2 = 26 and b) 15x2 = 30
Why 2? Because 13 is 2 units apart from 15.
So final answer is 225 - 30 - 26 = 169 = 13x13
This looks like a lot of task, because I have written down the steps. But see below how this can speed up the process for bigger numbers.
Lets consider 187x187.
I choose 185 as nearest number => Square of 185 = 34225
Now, since 187 > 185 => we'll add two numbers
34225 + (187x2) + (185x2) = 34225 + 374 + 370 = 34969 ---> Square of 187
E.g. 202x202
Choose 205 => 205x205 = 42025
42025 - (202x3) - (205x3) = 42025 - 606 - 615 = 40804 = 202x202
Once you are used to this, I am sure you will find this easier compared to the conventional way of multiplying which is error prone & time consuming.
In case you dont know how to calculate squares of numbers ending in 5, here it is:
e.g. 65
Take the last digit -> square it -> 5x5 = 25
take the remaining number and multiply by the next number -> 6x7 = 42
Place this number ahead of 25 --> 4225 --> square of 65
Please share if you have better ways of doing this. It would be helpful for people like me who make mistakes even while multiplying
I happened to discover (only if someone else hasn't shared this before
) a faster way of calculating squares of any number not ending in 0 or 5.Things you need to know: Shortcut to calculate squares of numbers ending in 5 (given at the end of post)
Suppose you have to calculate 13x13
Step1: Either choose the nearest number ending in 5, i.e. 15 or nearest number ending in 0, i.e. 10.
Let us suppose we choose 15
Step2: Square this number - 15x15
Use the shortcut to find squares ending in 5. You will get 225.
Step 3: Crucial step:
Now, since 13 is smaller than 15, you will subtract from 225 two numbers calculated as follows (Do the reverse, i.e. add when the number is bigger)
a) 13X 2 = 26 and b) 15x2 = 30
Why 2? Because 13 is 2 units apart from 15.
So final answer is 225 - 30 - 26 = 169 = 13x13
This looks like a lot of task, because I have written down the steps. But see below how this can speed up the process for bigger numbers.
Lets consider 187x187.
I choose 185 as nearest number => Square of 185 = 34225
Now, since 187 > 185 => we'll add two numbers
34225 + (187x2) + (185x2) = 34225 + 374 + 370 = 34969 ---> Square of 187
E.g. 202x202
Choose 205 => 205x205 = 42025
42025 - (202x3) - (205x3) = 42025 - 606 - 615 = 40804 = 202x202
Once you are used to this, I am sure you will find this easier compared to the conventional way of multiplying which is error prone & time consuming.
In case you dont know how to calculate squares of numbers ending in 5, here it is:
e.g. 65
Take the last digit -> square it -> 5x5 = 25
take the remaining number and multiply by the next number -> 6x7 = 42
Place this number ahead of 25 --> 4225 --> square of 65
Please share if you have better ways of doing this. It would be helpful for people like me who make mistakes even while multiplying
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