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The two square roots of a negative number are both imaginary numbers, and the square root symbol refers to the principal square root, the one with a positive imaginary part. For the definition of the principal square root of other complex numbers, see Square root § Principal square root of a complex number.
The square root of a positive integer is the product of the roots of its prime factors, because the square root of a product is the product of the square roots of the factors. Since p 2 k = p k , {\textstyle {\sqrt {p^{2k}}}=p^{k},} only roots of those primes having an odd power in the factorization are necessary.
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√ (square-root symbol) Denotes square root and is read as the square root of. Rarely used in modern mathematics without a horizontal bar delimiting the width of its argument (see the next item). For example, √2. √ (radical symbol) 1. Denotes square root and is read as the square root of.
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Created with gnuplot using the following input file: set terminal svg font "Bitstream Vera Sans,18" size 600,300 set output "Square_root.svg" set xrange [0:25] set yrange [0:5] set xzeroaxis linetype -1 set yzeroaxis linetype -1 set xtics axis nomirror set ytics axis nomirror set mxtics 5 set key off set grid set border 0 set samples 400 plot x**0.5 with line linetype rgbcolor "red" linewidth 2
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unstrict inequality signs (less-than or equals to sign and greater-than or equals to sign) : 1670 (with the horizontal bar over the inequality sign, rather than below it) ...