What is a radical conjugate?
1 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))1+√32+√3
we want to rationalise the denominator
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)-11+√32+√3=1+√32+√3⋅2−√32−√3=√3−14−3=√3−1
This is one use of the difference of squares identity:
a^2-b^2 = (a-b)(a+b)a2−b2=(a−b)(a+b)
Specifically:
a^2-b^2c = (a-bsqrt(c))(a+bsqrt(c))a2−b2c=(a−b√c)(a+b√c)
A complex conjugate is actually a special case of the radical conjugate in which the radical is
