# What is a radical conjugate?

##### 1 Answer

May 19, 2016

#### Answer:

Assuming that this is a maths question rather than a chemistry question, the radical conjugate of

#### Explanation:

When simplifying a rational expression such as:

#(1+sqrt(3))/(2+sqrt(3))#

we want to rationalise the denominator *radical conjugate*

So we find:

#(1+sqrt(3))/(2+sqrt(3))=(1+sqrt(3))/(2+sqrt(3))*(2-sqrt(3))/(2-sqrt(3))=(sqrt(3)-1)/(4-3) = sqrt(3)-1#

This is one use of the difference of squares identity:

#a^2-b^2 = (a-b)(a+b)#

Specifically:

#a^2-b^2c = (a-bsqrt(c))(a+bsqrt(c))#

A *complex conjugate* is actually a special case of the radical conjugate in which the radical is