Astraphobia immediately identified as a phobia because children naturally go through many fears as they mature. Their fear of thunder and lightning cannot be considered a fully developed phobia unless it persists for more than six months. In this case, the child's phobia should be addressed, for it may become a serious problem in adulthood. To lessen a child's fear during thunderstorms, the child can be distracted by games and activities. A bolder approach is to treat the storm as an entertainment; a fearless adult is an excellent role model for children. The most widely used and possibly the most effective
Quadratic irrational number expressed as for integers ; with , and non-zero, and with square-free. When is positive, we get real quadratic irrational numbers, while a negative gives complex quadratic irrational numbers which are not real numbers. This implies that the quadratic irrationals have the same cardinality as ordered quadruples of integers, and are therefore countable. Quadratic irrationals are used in field theory to construct field extensions of the rational field . Given the square-free integer , the augmentation of by quadratic irrationals using produces a quadratic field ). For example, the inverses of elements of ) are of the same form as