Radical symbol

The radical symbol is a special sign used in mathematics to show the square root of a number. It looks like a checkmark with a line above it. For example, the square root of 9 is written as √9 and equals 3, because 3 × 3 = 9.

This symbol can also be used for other roots. The nth root of a number x is written with the number n above the radical symbol, like this: √[n]{x}. For instance, the cube root of 8 is written as √{8} and equals 2, because 2 × 2 × 2 = 8.

Besides mathematics, the radical symbol is also used in linguistics to show the root of a word. This is the basic part of the word that gives it its meaning. For example, the root of the word "happy" is "hap".

Principal square root

Every positive real number has two square roots: one positive and one negative. The radical symbol shows the principal square root, which is the positive one. For negative numbers, both square roots are imaginary numbers, and the symbol refers to the one with a positive imaginary part. For more details on complex numbers, see the section on the principal square root of a complex number.

Origin

The symbol for square roots, √, has an interesting history. Some think it came from an Arabic letter that means "root." Others believe it came from a Latin word, "radix," also meaning "root."

The symbol we use today first appeared in a book in 1525 by a German mathematician named Christoff Rudolff. Later, in 1637, Descartes added a bar to make the symbol we know now.

Encoding

The radical symbol shows square roots and other roots in math. It has special codes so computers can display it correctly. For example, the square root symbol has a code called U+221A. Sometimes it looks different from how it appears in math books because it might not include a line above the number.

Different computer systems and fonts use various ways to show these symbols. Some older systems have their own special codes for the square root symbol, too.