Pronunciation: [ɹˈadɪkə͡l nˈʌmbə] (IPA) 
The correct spelling of the term "radical number" is /ˈrædɪk(ə)l ˈnʌmbə/. The word "radical" is spelled with an "a" after the letter "d" to indicate the short vowel sound in the first syllable. The word "number" is spelled with an "m" after the letter "n" to indicate the bilabial nasal sound. A radical number is a number that is expressed using a radical symbol (√), which signifies a square root or other types of roots.
A radical number refers to a mathematical expression that consists of a radical symbol (√) along with a numerical value under the symbol. It is also known as a square root or a radical. The numerical value under the symbol is referred to as the radicand, while the whole expression is called a radical.
The radical symbol (√) represents the operation of finding the square root of a number, which is the value that, when multiplied by itself, gives the original number. For instance, in the radical number √9, 9 is the radicand, and the square root of 9 is 3 since 3 multiplied by itself equals 9.
Radical numbers can also include other roots such as cube roots (∛) or higher order roots. These symbols indicate finding the number that, when multiplied by itself a certain number of times, yields the radicand. For example, ∛27 is a radical number, with 27 as the radicand and 3 as the cube root since 3 multiplied by itself three times equals 27.
Radical numbers are closely related to irrational numbers, as the square roots of most whole numbers are irrational. However, not all radical numbers are irrational, as some radicands have rational square roots. Radical numbers have numerous applications in different branches of mathematics, physics, engineering, and other scientific fields.
The term "radical number" does not have a specific etymology as it is a combination of two different concepts.
The word "radical" originates from the Latin word "radix" which means "root". In mathematics, a radical is a symbol (√) used to represent the square root or nth root of a number.
On the other hand, the word "number" originates from the Latin word "numerus", meaning "a quantity". It has been used to refer to numerical figures since ancient times.
When combined, "radical number" refers to a mathematical concept involving the square root or nth root of a number. However, it is worth mentioning that in common usage, the term "radical" is more commonly used to refer to a person or idea advocating for drastic or extreme social or political change rather than for mathematical purposes.
