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 Post subject: Finding square root of ...Posted: Tue Mar 04, 2014 11:41 pm

Joined: Mon Mar 08, 2010 1:03 pm
Posts: 1413
Can anyone tell me how one finds the square root of, say, a 3 digit number such as 169? DS did it by playing about with large numbers until he found that 13x13 got the desired answer. But is there a more efficient, time-saving way of figuring it out?

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 Post subject: Re: Finding square root of ...Posted: Wed Mar 05, 2014 12:44 am

Joined: Wed Aug 01, 2007 11:19 am
Posts: 888
If you know it's a whole number -

169<400 so it's less than 20

Then think about the last digit - 9. What (one digit) number squared gives you something that ends in 9? 3*3=9, 7*7=49

So you've narrowed it down to 13 or 17. You could say that 169 is nearer to 100 than 400 so it's probably 13, or you could just work those two out to check.

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 Post subject: Re: Finding square root of ...Posted: Wed Mar 05, 2014 6:36 am

Joined: Tue Jul 21, 2009 9:56 pm
Posts: 8228
Yes, that's a good way. We learned all our square numbers up to 25 x 25 off by heart. It was useful.

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 Post subject: Re: Finding square root of ...Posted: Wed Mar 05, 2014 7:14 am

Joined: Wed Aug 01, 2007 11:19 am
Posts: 888
I think for GCSE the suggestion is that you know 1-15 squared, and then 1, 2, 3, 4, 5, 10 cubed.

Knowing how to get from one square to the next e.g. knowing that 12x12=144 to 13x13 is useful: 144 + 12 + 13 = 169

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 Post subject: Re: Finding square root of ...Posted: Wed Mar 05, 2014 10:38 am

Joined: Mon Mar 08, 2010 1:03 pm
Posts: 1413
Thanks Aliportico and Mystery. V useful advice.

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 Post subject: Re: Finding square root of ...Posted: Wed Mar 05, 2014 10:51 am

Joined: Mon May 16, 2011 1:05 pm
Posts: 4019
I was taught a method for finding square roots when I was about 10. I can't remember it but it was a similar layout to long division.

I have never found anyone else who knows it to reteach me.

I'll go back to my slide rule now. (Yes I really do have one, freaks out the grads)

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 Post subject: Re: Finding square root of ...Posted: Wed Mar 05, 2014 11:02 am

Joined: Tue Dec 18, 2012 10:59 am
Posts: 3579
Quote:
Knowing how to get from one square to the next e.g. knowing that 12x12=144 to 13x13 is useful: 144 + 12 + 13 = 169

I have just learnt this!

I asked my ds1 if he knew it , he Said he just knew his square roots to 20..then proved it!

I then asked him how it worked, and he said without even looking, it just does, who cares, if it works use it!

Told ds2, who is more his mother's son, and he immediately said "how"

I kind of see it of course, but would love a proper explanation please, to relay simply to ds2, as a blathered this morning like mums on the hoof do.

Tinkers, I bet my steel slide rule is older than yours, I have my dad's...it has 12th' s on the top line, with a smaller metric line below! It also has a grease line where he kept it sliding using something yukky and oily.

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 Post subject: Re: Finding square root of ...Posted: Wed Mar 05, 2014 12:20 pm

Joined: Sat Aug 10, 2013 11:46 am
Posts: 188
I don't know if this is a proper mathematical proof, but if you get some graph paper and draw out a 12*12 square, to make it into a 13*13 square you have to add one length of 12 squares along the bottom edge and another length of 12 squares down the right hand edge. Then there is one more square to add in the corner where they meet.

Another way of working out non prime square roots is to see if you can divide the number. For example, suppose you had no idea the what the square root of 144 was. You could divide by 9 to get 144/9=16.
Therefore 144=9*16.
So square root of 144=(square root of 9)*(square root of 16)=3*4=12

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 Post subject: Re: Finding square root of ...Posted: Wed Mar 05, 2014 12:47 pm

Joined: Wed Aug 01, 2007 11:19 am
Posts: 888
12x12=144
12x13=156

And I don't know the way you mention Tinkers, but I know it exists and I'd like to know it too!

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 Post subject: Re: Finding square root of ...Posted: Wed Mar 05, 2014 12:51 pm

Joined: Tue Dec 18, 2012 10:59 am
Posts: 3579

Ok, it was the reverse I was leaving out, I will tackle it again with him tonight...thank you.

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