Surds and irrational equations

Surds extend the notion of a power: writing $\sqrt[n]{a}$ is the same as writing $a^{1/n}$, and this equivalence lets us apply all the rules of powers to roots as well. The chapter introduces the structure of a surd together with its existence conditions, the operations between surds and the techniques for manipulating them (taking factors out of the radical sign, reducing to the same index, rationalising the denominator). From here we move on to irrational equations, where the unknown appears under a root and squaring can introduce extraneous solutions, and to inequalities with a square root, reduced to two fundamental schemes. The chapter closes with a reference to probability (covered in the fourth year) and an introduction to linear regression by the method of least squares.

Sections

• Surds and powers with a fractional exponent
• Rationalising the denominator
• Irrational equations
• Inequalities with a square root
• Linear regression
• Probability (reference to the fourth year)

Exercises

• All the chapter’s exercises