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Radical

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The symbol RadicalBox[x, n] used to indicate a root is called a radical, or sometimes a surd. The expression RadicalBox[x, n] is therefore read "x radical n," or "the nth root of x." In the radical symbol, the horizonal line is called the vinculum, the quantity under the vinculum is called the radicand, and the quantity n written to the left is called the index.

In general, the use of roots is equivalent to the use of fractional exponents as indicated by the identity

(RadicalBox[x, p])^q=x^(p/q),
(1)

a more generalized form of the standard

RadicalBox[x, n]=x^(1/n).
(2)

The special case RadicalBox[x, 2] is written sqrt(x) and is called the square root of x. RadicalBox[x, 3] is called the cube root.

Some interesting radical identities are due to Ramanujan, and include the equivalent forms

(2^(1/3)+1)(2^(1/3)-1)^(1/3)=3^(1/3)
(3)

and

(2^(1/3)-1)^(1/3)=(1/9)^(1/3)-(2/9)^(1/3)+(4/9)^(1/3).
(4)

Another such identity is

(5^(1/3)-4^(1/3))^(1/2)=1/3(2^(1/3)+20^(1/3)-25^(1/3)).
(5)

See also

Cube Root, Index, nth Root, Nested Radical, Power, Radical Center, Radical Circle, Radical Integer, Radical Line, Radicand, Square Root, Surd, Ultraradical, Vinculum

Portions of this entry contributed by Christopher Stover

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References

Wolfram, S. A New Kind of Science. Champaign, IL: Wolfram Media, p. 1168, 2002.

Referenced on Wolfram|Alpha

Radical

Cite this as:

Stover, Christopher and Weisstein, Eric W. "Radical." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Radical.html

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