is the square root of 3 rational
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The square root of 37 is an irrational number
√37 is irrational.
It is an irrational number
The same reasoning you may have seen in high school to prove that the square root of 2 is not rational can be applied to the square root of any natural number that is not a perfect square.
No, the square root of 1500 is not a rational number.