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