Yes; there are some lengths that can be measured but not described by the form a/b, where a and b are integers. For example, a right triangle with legs of length 1 has a hypotenuse of the square root of 2, which is an irrational number.
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Yes. 3/sqrt(2) is an irrational number and so cannot be round.
It is irrational. Any number that cannot be written as a fraction is irrational. So if the Golden Ratio were rational, instead of a never-ending decimal number, you'd see a fraction. The official measurement is (1+sqrt5)/2. sqrt5 is irrational.
That 's not possible since irrational numbers have infinity digits. All whole numbers are rational.
+sqrt(47) is one possible answer.
An irrational number.