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You can't prove this proposition because it isn't true.
Proof: the fifth root of 1024 is 4, and 4 is not irrational.
It is true that, when N is an integer greater than 1, the Nth root of any integer greater than 1 is either an integer orirrational, but that's a different matter.
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Is the square root of a 143 a 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.
Is the square root of 10 rational or irrational?
Square root of 10 is irrational.
Why is the square root of 10 irrational?
The argument why the square root of 2 is irrational can be found in most high school algebra books. You can also find this proof, and several other proofs, that the square root of 2 is irrational, in the Wikipedia article "Square root of 2".The same argument can be applied to the square root of any natural number that is not a perfect square.
How do you prove that root 2 root 3 is an irrational number?
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.
Is the square root of 45 rational or irrational?
It is irrational
