It is known that the square root of an integer is either an integer or irrational.
If we square root2 root3 we get 6. The square root of 6 is irrational.
Therefore, root2 root3 is irrational.
Yes. The square root of a positive integer can ONLY be either:* An integer (in this case, it isn't), OR * An irrational number. The proof is basically the same as the proof used in high school algebra, to prove that the square root of 2 is irrational.
(root 2)/3
The square root of 2 times the square root of 2 is rational.
Yes. The square of a whole number is always a whole number. For example, 3 squared is 9, so the square root of 9 is 3. What you never have, is the square root of a whole number being a fraction that is not a whole number. The square root of a whole number is either a whole number or an irrational number. For example, the square root of 2 is irrational, because there are no 2 whole numbers a and b such that a/b squared is 2. This is not terribly difficult to prove, but I have already said too much; I have answered your question.
It is rational. The root of a perfect square, such as 4, is rational; the root of any positive integer that is not a perfect square is an irrational number.
The square root of 2 is 1.141..... is an irrational number
This is impossible to prove, as the square root of 2 is irrational.
I linked a good resource that explains what you asked below.
No; you can prove the square root of any positive number that's not a perfect square is irrational, using a similar method to showing the square root of 2 is irrational.
Yes, the square root of 2 is an irrational number.
Yes. The square root of a positive integer can ONLY be either:* An integer (in this case, it isn't), OR * An irrational number. The proof is basically the same as the proof used in high school algebra, to prove that the square root of 2 is irrational.
The square root of 2 is an irrational number
2 is a prime number and its square root is an irrational number that cannot be expressed as a fraction
irrational
No, the square root of an irrational number is not always rational. In fact, the square root of an irrational number is typically also irrational. For example, the square root of 2, which is an irrational number, is itself irrational. However, there are exceptions, such as the square root of a perfect square of an irrational number, which can be rational.
Yes. For example, the square root of 3 (an irrational number) times the square root of 2(an irrational number) gets you the square root of 6(an irrational number)
Yes, they are irrational.