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The '''square root''' of a number ''X'' is the number that, multiplied by itself, results in ''X''. <!-- The symbol for the square root of ''X'' is <math>sqr(X)</math>. --> Many computer languages and spreadsheet programs use "''sqr(X)''" to express this, as do people when mathematical symbols are not conveniently available.
The '''square root''' of a number ''X'' is the number that, multiplied by itself, results in ''X''. The symbol for the square root of ''X'' is <math>\sqrt{X}</math>. Many computer languages and spreadsheet programs use "''sqr(X)''" to express this, as do people when mathematical symbols are not conveniently available.
Some square roots are relatively simple [[whole number|whole numbers]], for example, 3 is the square root of 9. Others are less amenable to expression, such as the square root of 2 (1.414...), which has been proven to be an [[irrational number]].
Some square roots are relatively simple [[whole number|whole numbers]], for example, 3 is the square root of 9. Others are less amenable to expression, such as the square root of 2 (1.414...), which has been proven to be an [[irrational number]].
Negative numbers have square roots that lie outside the [[real number|real numbers]], and involve what are called [[imaginary number|imaginary numbers]], constructed via use the square root of -1, which is labelled ''i''. Thus, the square root of -9 is 3''i''.
Negative numbers have square roots that lie outside the [[real number|real numbers]], and involve what are called [[imaginary number|imaginary numbers]], constructed via use the square root of -1, which is labelled ''i''. Thus, the square root of -9 is 3''i''.
Technically, all numbers have two square roots, one positive and the other negative, since sqauring the negative number results in a positive number. Thus, sqr(9)=plus or minus 3, written +/-3; likewise the sqr(-9) = +/-3''i''.
Technically, all numbers have two square roots, one positive and the other negative, since sqauring the negative number results in a positive number. Thus, sqr(9)=plus or minus 3, written +/-3; likewise <math>\sqrt(-9) = +/-3i</math>.
The square root of a number can also be denoted as ''X''<sup>1/2</sup>, or ''X''^(1/2) if superscript is not available. This can readily be seen by the rule of adding powers when multiplying: ''X''<sup>1/2</sup> <math>*</math> ''X''<sup>1/2</sup> = ''X''<sup>1/2+1/2</sup> = ''X''<sup>1</sup> = ''X''.
The square root of a number can also be denoted as <math>X^{\frac{1}{2}}</math>, or ''X''^(1/2) if superscript is not available. This can readily be seen by the rule of adding powers when multiplying: ''X''<sup>1/2</sup> <math>*</math> ''X''<sup>1/2</sup> = ''X''<sup>1/2+1/2</sup> = ''X''<sup>1</sup> = ''X''.