Assertion: real number's root | /r/HasProperty | irrational number
Facets:
value: in all other cases
type: OTHER
value: always
type: DEGREE
Source sentences:
text: So, the square root of 2 (√2) is an irrational number.
text: Many square roots, cube roots, etc are also irrational numbers.
text: When one needs to find the roots of an equation, such as for a quadratic equation, one can use the discriminant to see if the roots are real, imaginary, rational or irrational.
text: When one needs to find the roots of an equation, such as for a quadratic equation, one can use the discriminant to see if the roots are real, imaginary, rational or irrational.
text: Any square root that is not a perfect root is an irrational number.
text: For example, the square root of 2 is an irrational number, but it is not a transcendental number as it is a root of the polynomial equation x2 − 2 = 0.
text: Any square root that is not a perfect root is an irrational number.
text: Mathematicians have proved that the square root of every natural number is either an integer or an irrational number.
text: It was known to the ancient Greeks that square roots of positive whole numbers that are not perfect squares are always irrational numbers: numbers not expressible as a ratio of two integers (that is, they cannot be written exactly as m/n, where m and n are integers).
text: In all other cases, the square roots of positive integers are irrational numbers, and therefore their decimal representations are non-repeating decimals.
text: In all other cases, the square roots of positive integers are irrational numbers, and therefore their representations in any standard positional notation system are non-repeating.
text: The square root of x is rational if and only if x is a rational number that can be represented as a ratio of two perfect squares.
text: Which square roots are rational?
text: Among irrational numbers are the ratio π of a circle's circumference to its diameter, Euler's number e, the golden ratio φ, and the square root of two; in fact all square roots of natural numbers, other than of perfect squares, are irrational.
text: The square roots of all natural numbers which are not perfect squares are irrational and a proof may be found in quadratic irrationals.