Question native Cheryl, a teacher:

Does every number have actually a square root?

Hi Cheryl,

Negative number don"t have square roots. If a number is confident its square is positive, if it is negative its square is positive and if that is zero its square is zero. Thus there is no number who square is negative.

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For optimistic numbers, also positive integers, the answer is no so clear and also some the the background is fascinating. In the history of numbers the integers came first, in fact we may come into the human being with part integers developed in. Research by psychologists has displayed that babies, as young as 3 or four days old, can tell the difference in between collections the two and also three items.<1> If her number civilization is the human being of integers then no every number has actually a square root. Over there is no integer who square is 2.

The Greeks that Pythagoras" time to be comfortable with the square source of 2 because they might construct it. If you have a square figure with side length of 1 unit and the diagonal has length d units then then using Pythagoras" organize

12 + 12 = d2

Thus d2 = 2 and hence d is the square source of 2. In reality not only is the square root of 2 not an integer that is not also a rational number. Probably the first person that realized the root 2 is irrational was Hippasus, among the of the practical worker of Pythagoras. Legend has it the Hippasus make his exploration at sea and was thrown overboard through fanatic Pythagoreans<2>. For this reason if her number people is the world of rational number then no every number has actually a square root. There is no reasonable number who square is 2.

This trouble is among the reasons that mathematicians defined the real numbers. If your number human being is the people of genuine numbers climate every non-negative number has a square root.

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I hope this helps,Harley

Math central is supported by the university of Regina and The Pacific Institute for the mathematics Sciences.