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{{ printedBook.courseTrack.name }} {{ printedBook.name }} The square root of a number $a,$ which is written as $a $, is the positive number that when multiplied by itself equals $a.$ Below is an example. $16 =4because4⋅4=16$ Square roots and raising a number to the $2$nd power are operations that undo each other.

$a ⋅a =aor(a )_{2}=a$

The square root as an object and as a process are consider distinct mathematical ideas. As an object, a square root is always positive. For instance, $16 =+4$
because this refers to the *principle root* of $16$ has been established. This convention removes all ambiguity. However, the square root as an operation takes both positive and negative values. Consider the equation $x_{2}=9.$
To solve for $x,$ the square root of both sides of the equation must be taken. $x_{2} =9 $
The values of $x$ that make the above equation true are $3$ and $-3$ because
$3_{2}=9and(-3)_{2}=9.$

The square root of a negative number cannot be a real number. This is because there is no real number that exists such that when it is multiplied by itself, a negative value is produced. $(+a)⋅(+a)=a_{2}and(-a)⋅(-a)=a_{2}$ Instead, the square roots of negative numbers produce imaginary numbers.