square root of square root binomial

Some people call the expressions of the form  a+bc  the , especially when c is an square-free integer greater than 1 (and a and b rational numbersPlanetmathPlanetmathPlanetmath).  On the high school (see e.g. division), or also polynomialsPlanetmathPlanetmath containing several square root .  Taking the square root of a square root binomial is more difficult and usually results nested square roots.  However, there are some exceptions if the numbers are appropriate.  We have the




If  a2-b  happens to be square of a rational number, then the into expressions without nested square roots.

For example, because  62-20=16=42,  we obtain


and because  42-7=9=32,  we get



  • 1 K. Väisälä: Algebran oppi- ja esimerkkikirja I.   – Werner Söderström osakeyhtiö, Porvoo & Helsinki (1952).
Title square root of square root binomial
Canonical name SquareRootOfSquareRootBinomial
Date of creation 2013-03-22 15:21:21
Last modified on 2013-03-22 15:21:21
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 10
Author pahio (2872)
Entry type Topic
Classification msc 11A25
Related topic TakingSquareRootAlgebraically
Related topic SquareRootsOfRationals
Defines square root binomial
Defines square root polynomial