Changing the Subject and Manipulating Surds

Two other types of useful algebraics skills and techniques are changing the subject of a formula and dealing with surds and roots.

Changing the Subject

Often a formula will contain several variables and will require re-arrangement to make a particular variable the subject of the formula.

Simple Example
Harder Example

Make x the subject of the equation 2y = 3x − 2

2y = 3x − 2

3x = 2y + 2

x = Y12_Changing_the_Subject_and_Manipulating_Surds_01.gif

Make b the subject of the formula Y12_Changing_the_Subject_and_Manipulating_Surds_02.gif



Surds are irrational terms or numbers given in the form of a root. e.g. √3
Surds can be manipulated using the usual rules of algebra.


(√3 + 2)(√3 − 2) = 3 + 2√3 − 2√3 − 4 = -1

Rationalisation of Surds

Algebraic fractions containing surds or roots in the denominator should be rationalised. e.g. The surds should be removed.
To do this the fraction is multiplied, top and bottom, by a similar surd expression with a different sign.


Rationalise the denominator of the expression Y12_Changing_the_Subject_and_Manipulating_Surds_04.gif.


Solving of Surd Equations

Equations involving surds and roots can often be solved by squaring each side of the equation. Sometimes the equations need re-arranging first. If there is more than one answer, it is necessary to check each answer as on occassions an answer may be a false solution.


Solve the equation √(2x) = √(x + 1)

Square both sides

[√(2x)]2 = [√(x + 1)]2

2x = x + 1

x = 1