# The Naked Scientists Forum

### Author Topic: 5th root if integer number by hand?  (Read 3977 times)

#### towi

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##### 5th root if integer number by hand?
« on: 14/09/2010 12:19:10 »
Hi,

I can vaguely remember that someone amazed me once that he could calculate the 5th root of a natural number that I had to write down for him. I just had to promise that the result is a regular integer as well, then he would stare at the number for a couple of seconds and then he told me the result. It was not a math genius or so, a normal student. I think the numbers I presented him were like 1027^5 and such.

What is the trick? I know of many tricks, how to check for dividability-by-three ans so on, but the 5th root?

thanks!

towi.

#### imatfaal

• Neilep Level Member
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##### 5th root if integer number by hand?
« Reply #1 on: 14/09/2010 13:18:16 »
Hi Towi

there is a trick for reasonable small 5th roots (ie so that root is only two figures)  - I will dig it out and forward link.

if i remember correctly it relies on the fact that the unit digit of a fifth power is always the same as the unit of the 5th root, coupled with learning some intervals of the large part of the number that allow you to know the tens digit of the root.

Your example 1027 gives a 16 digit 5th power - and I dont know any trick to work that out.

#### imatfaal

• Neilep Level Member
• Posts: 2787
• rouge moderator
##### 5th root if integer number by hand?
« Reply #2 on: 14/09/2010 16:03:30 »
Towi

Found it almost straight away http://www.curiousmath.com/index.php?name=News&file=article&sid=74

A quick check will note that the list has a typo: 2 in the tens column relates to numbers greater than 320 ...

#### The Naked Scientists Forum

##### 5th root if integer number by hand?
« Reply #2 on: 14/09/2010 16:03:30 »