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Examples of Irrational Numbers which are not square roots of whole numbers are pi (3.14159 to five decimal places), the golden ratio (1.6180339887...) and silver ratio (2.4142135623), and the twelfth root of two, which is the difference between any two notes in an even-tempered musical scale.

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Is the square root of a irrational number always rational?

No, the square root of an irrational number is not always rational. In fact, the square root of an irrational number is typically also irrational. For example, the square root of 2, which is an irrational number, is itself irrational. However, there are exceptions, such as the square root of a perfect square of an irrational number, which can be rational.


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