[math]\sqrt3\times\sqrt{27}=\sqrt{81}=9[/math], a rational number. [math]\sqrt3\div\sqrt{27}=\frac{\sqrt3}{3\sqrt3}=\frac13[/math], also a rational number. What do you mean by “by”? read more
No, the square root of 3 is not rational.No. The square root of 3 is irrational.More generally: if p is a prime number then the square root of p is irrational and the proof of this fact mimics the famous proof of irrationality of the square root of 2.No - the square root of 3 is not rational, but the proof is tooinvolved to post here. read more