Difference between revisions of "Square roots are always nonnegative"
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| − | + | Many people get confused, thinking that <math>x^2 = 16</math> and <math>x= \sqrt{16}</math> are the same. Though both of these are similar, one of them only has one answer. If we take <math>x^2 = 16</math>, we can see that it has <math>2</math> answers; <math>4</math> and <math>-4</math>. On the other hand, <math>x = \sqrt{16}</math> only has one. | |
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'''Square Root''' is a function, and a function cannot have two different answers for one input. Technically <math>-4</math> and <math>4</math> are "square roots" of <math>16</math>, but the square root function only represents one of them--the ''nonnegative'' answer. | '''Square Root''' is a function, and a function cannot have two different answers for one input. Technically <math>-4</math> and <math>4</math> are "square roots" of <math>16</math>, but the square root function only represents one of them--the ''nonnegative'' answer. | ||
Latest revision as of 13:51, 16 May 2025
Many people get confused, thinking that 
and 
are the same. Though both of these are similar, one of them only has one answer. If we take , we can see that it has 
answers; 
and 
. On the other hand, 
only has one.
Square Root is a function, and a function cannot have two different answers for one input. Technically and are "square roots" of 
, but the square root function only represents one of them--the nonnegative answer.
