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
-
Identify the surd in the denominator of the fraction that needs to be rationalised.
-
Multiply both the numerator and denominator of the fraction by the surd.
-
Carry out the multiplication in each part of the fraction separately.
-
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.