What is a Radical
Radical is a math symbol for the root of a number. The most basic radical symbol is the square root.
Components of a Radical
Radical Symbol: √
Root: The number within radicals.
Index: Root index (Square root, Cube root, etc.) They then follow with an appropriate number indicating the index number (for example, the index is 2 (the square root) and so is not written, as is the case in √9 , while for a larger root, the cube root, it will be written: ∛8
NOTE: If no index is written, it is assumed to be a square root (index of 2).
Examples
√ 16= 4 because 4× 4=16
³√27=3 because 3×3×3=27
⁴√ 81=3 because 3×3×3×3=81
Radicals are used in various fields, including geometry (e.g., calculating distances using the Pythagorean theorem), physics, engineering, and statistics.
√a*√b=√(ab)
√a÷√b=√(a÷b)
ⁿ√(aᵐ)=aⁿ÷ᵐ
Reflection:
There are several forms of radicals: square roots, cube roots, and higher-order roots. They are basic expressions that appear in algebra and mathematics generally. They let us take a number out of its "root form" and expose, if you will, its essential nature-that is, some number that, when multiplied by itself a certain number of times, gives some other value. There is an art to handling radicals, and that art involves familiarity with the properties of radicals and their behavior under the standard operations of addition, subtraction, multiplication, and division.