Square root problem?

Original post by CormacMcGowan

Has anyone found a way too find the square root without a calculator :argh:

There's an algorithm a bit like long division for working out square roots manually. I don't know if it has a name and I'm too lazy to type out the details now, but basically you start by pairing off the digits, estimating a square root for the 1st pair of digits (which is easy cos you're only looking at 00 - 99), then bringing down successive pairs of digits and trying to form a product (x + d) * d which is less than or equal to your "running total" and finding the maximum value of digit d for which this works!

It's a lot easier to do than to explain!

Reply 4

GCSEsitter

8

Do it in your head by estimating based on values you already know e.g & for root12 it is between 9 and 16 so will be around 3.5. Hope this helps

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(edited 9 years ago)

Original post by davros

There's an algorithm a bit like long division for working out square roots manually. I don't know if it has a name and I'm too lazy to type out the details now, but basically you start by pairing off the digits, estimating a square root for the 1st pair of digits (which is easy cos you're only looking at 00 - 99), then bringing down successive pairs of digits and trying to form a product (x + d) * d which is less than or equal to your "running total" and finding the maximum value of digit d for which this works!

It's a lot easier to do than to explain!

Here is a worked example.

Reply 6

Original post by Mr M

Here is a worked example.

PRSOM

Excellent - I found it in a book over 30 years ago, no idea where, but hadn't seen it online before (not that I'd looked terribly hard).

Reply 7

Matureb

19

Would you have seen it here?

http://www.amazon.co.uk/Trachtenberg-Speed-System-Basic-Mathematics/dp/0285629166

This is where I found it, but never understood it

See pages 197+

(edited 9 years ago)

Reply 8

Original post by Matureb

Would you have seen it here?

http://www.amazon.co.uk/Trachtenberg-Speed-System-Basic-Mathematics/dp/0285629166

This is where I found it, but never understood it

See pages 197+

It doesn't ring any bells, but it's possible as it was so long ago!

Local libraries used to contain hundreds of maths books - now you're lucky if they old more than about 15-20 :smile:

Reply 9

What's wrong with just using surds??

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Reply 10

Original post by Physika

What's wrong with just using surds??

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I think you may have missed the point of some of the posts (although it's not entirely clear what answer the OP was expecting anyway :smile:

)

Reply 11

I get the point but it kind of obsolete don't you think I mean there is no point in fining the numerical answer because you will always have errors, for example root 2 is irrational and the only way of presenting it exactly would be root2

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Reply 12

BabyMaths

Original post by Physika

I get the point but it kind of obsolete don't you think I mean there is no point in fining the numerical answer because you will always have errors, for example root 2 is irrational and the only way of presenting it exactly would be root2

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A numerical value is often useful and we can make it as accurate as necessary.

These days doing awkward calculations without a calculator or computer is just for fun. :tongue:

Reply 13

Honestly am a big fan of mental maths, but I hate the application of numerical methods such as the newton rap halon method which was mentioned before. Of course you can get as accurate as necessary but there will be a situation where even a 0.01% error could not be considered negligible so in my mind fractions and surds just work better for me. But that is just personal preference, and obviously 99% of the time numerical methods are perfectly acceptable.

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Reply 14