the number 529

Accidentally found out for some reason if you take the number 529 and raise it to any power*, then take the square root, the answer is always a whole number. I suppose there are other numbers like that, and it's probably not as amazing to everybody like it is to me

is this a type of number, a 'thing', like prime numbers are a thing?

* at least I haven't found a case where it doesn't work

the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!”   She is, after all, stone deaf. ... Arnold Snyder

Quote: odiousgambit

Accidentally found out for some reason if you take the number 529 and raise it to any power*, then take the square root, the answer is always a whole number. I suppose there are other numbers like that, and it's probably not as amazing to everybody like it is to me

is this a type of number, a 'thing', like prime numbers are a thing?

* at least I haven't found a case where it doesn't work

Setting up an Excel spreadsheet confirms your amazing result!

Quote: ChesterDog

Quote: odiousgambit

Accidentally found out for some reason if you take the number 529 and raise it to any power*, then take the square root, the answer is always a whole number. I suppose there are other numbers like that, and it's probably not as amazing to everybody like it is to me

is this a type of number, a 'thing', like prime numbers are a thing?

* at least I haven't found a case where it doesn't work

Setting up an Excel spreadsheet confirms your amazing result!

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But then 529 seemed familiar to me because I had memorized that 23 squared is 529.

And taking the square root of the power of a number is equivalent to raising the square root of a number to that power. Raising a whole number to whole number power will always produce a whole number answer.

Yup. In other words, works for 4 also. And 9, 16, 25, etc.

OK, didn't explore enough

but I had checked out cubing a number, then taking the square root of that ...

perhaps very few numbers will result in a whole number? but 529 does

Quote: odiousgambit

OK, didn't explore enough

but I had checked out cubing a number, then taking the square root of that ...

perhaps very few numbers will result in a whole number? but 529 does

odious is correct, example"

sqrt(529¹⁰¹ )= 342382404646349906057205801490874347335703752037431479791270728812115965406404621099504973295378976497369961620127288149768965118187148023

One might try using all sorts of odd exponents, and sqrt(529^m) will test out to be an integer.

But of course: sqrt(529^m) = 23^m. That is the trick.

yeah, tried 625, which is 25 squared

if you cube 625, then take the square root of that [of 244140625], you get an integer

your formula there nails it