Study Notes
Surds are the square roots of numbers that cannot be simplified into a whole or rational number. You can manipulate surds using specific rules.
- Rational Number — a number that can be expressed as a fraction of two integers. Example: 1/2, 3, 4.5
- Irrational Number — a number that cannot be expressed as a simple fraction. Example: π, √2
- Surd — a root that is irrational, often involving square roots of non-perfect squares. Example: √2, √19, 5√2
- Rationalising the Denominator — the process of eliminating surds from the denominator of a fraction. Example: Multiply both numerator and denominator by a conjugate to rationalise.
Exam Tips
Key Definitions to Remember
- Rational Number: A number that can be expressed as a fraction of two integers.
- Irrational Number: A number that cannot be expressed as a simple fraction.
- Surd: A root that is irrational.
Common Confusions
- Confusing rational numbers with irrational numbers.
- Forgetting to simplify surds in expressions.
Typical Exam Questions
- What is a surd? A root that is irrational, such as √2.
- How do you rationalise the denominator of a fraction with a surd? Multiply the numerator and denominator by the conjugate of the denominator.
- Simplify the expression √18 + √8. 3√2 + 2√2 = 5√2
What Examiners Usually Test
- Ability to simplify expressions involving surds.
- Skill in rationalising the denominator of fractions with surds.
- Understanding the difference between rational and irrational numbers.