Rationalising surds

Rationalising Surds: An Overview

  • A Surds are root expressions that cannot be simplified to remove the root symbol - they are irrational numbers.
  • Rationalising a surd means to manipulate it so that the root symbol is removed from the denominator of a fraction.

Rationalisation Process

  • The process of rationalising a surd usually involves multiplying both the numerator and denominator of a fraction by the same surd.
  • This process does not change the value of the fraction because multiplying a number by 1 (which is any number divided by itself) leaves the number unchanged.
  • The multiplication results in the surd being ‘moved’ to the numerator of the fraction.

Steps in Rationalising Surds

  1. Identify the surd in the denominator of the fraction that needs to be rationalised.

  2. Multiply both the numerator and denominator of the fraction by the surd.

  3. Carry out the multiplication in each part of the fraction separately.

  4. Simplify the resulting expression if possible.

Examples

  • In the case of the fraction 1/√2, the surd √2 is in the denominator. Multiply the fraction by √2/√2 to get √2/2.

  • With the fraction 5/√3, multiply it by √3/√3 to get 5√3/3.

  • For the fraction 7/(3+√2), multiply the fraction by (3-√2)/(3-√2) to get (21- 7√2)/7.

Conclusion

  • Rationalising surds is a method used to express irrational numbers in a form that is often easier to work with in algebra.
  • It is a key skill in managing algebraic expressions, especially in higher level Algebra.
  • Remember to practice this technique with various examples to sharpen your understanding and command of this process.