No. The square roots of perfect squares are rational.
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No.
In mathematics, an irrational number is any real number that cannot be expressed as a ratio of integers. Irrational numbers cannot be represented as terminating or repeating decimals.The square root of 31 is one such.
A square root is not a number system. Square roots of non-negative numbers may be rational or irrational, but they all belong to the set of real numbers. The square roots of negative numbers do not. To include them, the number system needs to be extended to the complex numbers.
All prime numbers have irrational number square roots, so if you try to find the square root of a non-perfect square number use them to simplify it. For example, ±√125 = ±√25*5 = ±5√5 (when you want to show both the square roots) √72 = √36*2 = 6√2 √-27 = √-9*3 = 3i√3
Because some of them are squares of rational numbers. So their square roots are the rational numbers.Thus if x is rational, then the square roots of x2, which are -x and +x are both rational.