3 Digit Squares - Sometimes it's faster not to think so much

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#1 21 August, 2016 - 16:13
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3 Digit Squares - Sometimes it's faster not to think so much


Haven't posted for a bit but I noticed something today that made me quite happy.

This begins with the assumption that you 2 digit squares are solid...

With regular practice I was using A^2 + 2AB + B^2 with good accuracy and reasonable time and being able to cross reference with 2 or 3 other easy methods depending on the opportunities presented by the numbers themselves BUT never at an impressive speed. I believe there is a definite advantage in practice learning the math BUT to be really fast I think less thinking is required.

For example:


Trivial case

109 ^2
1
#18
###81

mentally you skip the addition steps and practice concatenation instead -

1^2 =
1
9*2 = 18
1|18
9^2 = 81
118|81

11,881

or

425
4^2=16
16
2*4*25 = 200
16+2|00
25^2 = 625
1800+6|25
180,625

This may seem like a fine point but it removes a very big part of the think time required to get the solution in hand.
By taking the calculation load off it also reduces mental stress which I find to be a significant constraint to thinking these things through in situations that are not simply calculation practice.

23 August, 2016 - 13:04
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Joined: 5 years 8 months ago

Quote:
I believe there is a definite advantage in practice learning the math BUT to be really fast I think less thinking is required.

I agree.
I try to use this effect as follows:

If we take a^2 + 2ab + b^2, with the first digit as 'a' and the 2nd and 3rd digits as 'b', then the number fall like this:

a^2 | 2ab | b^2

Like you said:

Quote:
mentally you skip the addition steps and practice concatenation instead

Only if 2ab or b^2 is big (more than 2 digits) do we need to look at the carry and do a (small) addition.

Quote:
By taking the calculation load off it also reduces mental stress

This is key!
When you first start to do calculations like these there is a lot to keep in mind.
You have the intermediate total, any subtotal to add to and all the carries there might be.
It is easy to lose track of where you are going.

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