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It is true that the square root of a Prime number like 11 is never a whole number. But to say that that has never been proven is incorrect. The square root of any positive integer that is not a square number (the square of an integer) is always irrational, and that is relatively easy to prove. To prove that prime numbers are not square numbers is even easier. That is basically true by definition. If a number greater than 1 were a square number, its square root would be a factor other than 1 and itself; therefore, it would not be a prime number.
Answer 1
No - the square root of 11 is not a whole number. 11 is prime so it has no factors except itself and 1, anyways.
Any prime number has no square root that is a whole number or integer. (That postulate has not been proven, but it has not been disproven so it is accepted as true.)
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How do you find an irrational square root?
An irrational number is a number that never ends. An example of an irrational square root would be the square root of 11.
Is square root of -11 rational number?
The square root of negative 11 is an imaginary number, i.e., sqrt(-11) = sqrt(11) i where i is the imaginary unit = sqrt(-1). sqrt(11) is indeed irrational. In fact, the square root of any integer which is not a power of two is irrational.
What is the square root of 11 to the nearest whole number?
3 because the square hypotenuse of the root would equal the same as both digits added together plus 1 (1+1+1). I sure hope this helps you :)
Is a square root a rational number?
A square root is considered a rational number if the number inside the square root sign is a perfect square. In other words, if the square root of a number results in a whole number, then it is a rational number. For example, the square root of 9 is 3, which is a whole number, making it a rational number. However, if the square root results in a non-terminating, non-repeating decimal, then it is considered an irrational number.
Is square root 11 an integer or fraction?
Answer: Mixed number Answer: It is neither, in the sense that you can't write the square root of any positive integer (except for the square root of perfect squares) exactly as a fraction. You can only approximate it. In other words, it's an irrational number.
