Rationalisation is a technique that gets an important place in elementary mathematics. It helps to simplify mathematical expressions to a simpler form. The term "Rationalisation" means to make something more efficient. For example, it helps us make the equation reduced into a more effective and simpler form.
Surds, i.e., the numbers under roots such as √2 ,√3 ,√8 are irrational numbers. In order to rationalise them, we have to either multiply or divide the numbers with appropriate factors. We will learn those properly in this chapter. Rationalisation helps us to eliminate the imaginary number from the denominator or numerator of an algebraic fraction. Mainly that is nothing but the numerator, or the denominator will contain only rational numbers.
We become familiar with some important terms in this chapter are,
Radical is an expression that contains a root, be it a square root or a cube root. For example, <span>√x+y</span> is a radical.
The degree is the number of times the radicand is multiplied by itself. 2 stands for square root, 3 means cube root, 4th root, 5th root, etc. If nothing is mentioned, we can take it as the square root. Such as in the expression
A conjugate of a binomial is nothing but another binomial, the same, with the opposite sign between its two terms. Such as a conjugate of (x + y) is (x – y) or vice versa. So these 2 binomials are conjugates of each other.
This chapter discusses the rationalisation of monomial, binomial, trinomial radical or rationalising a cube root or nth root.