Square root of 11

Is square root of 11 an irrational number? How do you know from using a calculator? Thank you.

Well, I happen to know that if the square root of a natural number is NOT a whole number, then it is an irrational number. There are no other possibilities.

Of course you can't tell by the calculator. The calculator will show you 8 or 10 decimals, but you won't know from that if it's going to continue or not, or if it is periodical or not.

But pure mathematics and established, proven theorems will tell you that! : )

A proof that the square root of 2 is irrational

Lots of proofs of the same... plus one proving that any root is irrational if it's not a whole number

Proof that the square root of any prime is irrational

Comments

Linda Moran said…
Maria, this is Linda Moran. I write a lot of stuff about the math wars, and although I public school my kids, I'm a big supporter of home schooling.

I like your blog and am about to write a tag blog that includes yours.

(Blog tagging is a fun blogging game in which I'll be mentioning five interesting blogs in an entry, and then those five blog writers, if they feel like it, can each then write a blog entry that mentions five more bloggers.)

Hopefully I'll have it published tomorrow.

http://www.lindamoran.net/blog_teen

Regards, Linda Moran
ajay saini said…
nice article.....
Savannah G.V. said…
I am pretty sure some decimals are rational. A rational number is any number that can be written as a fraction of two integers. So an number like 2.6 is rational but not whole because it can be written as 12/10. The square root of 11 is not raition because it is an infinite decimal. If you're wondering I am a homeschooler too.
Savannah G.V. said…
The square root of 11 is irrational but not every non-whole number is. A rational number is defined as a number that can be expressed as a fraction of two integers. So, even though a number like 2.6 isn't whole it is rational because it can be epressed as 12/10. The square root of 11 is only irrational because its decimal answer is infinite.

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