Difference between revisions of "Square roots are always nonnegative"
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Many people around the world 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. | Many people around the world 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. | ||
Revision as of 21:08, 4 February 2025
Square roots are always nonnegative
Many people around the world 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.
