Summary
Indices and surds involve operations with powers and roots, which are fundamental in mathematics.
- Power — when a number is multiplied by itself several times, it is expressed as a power. Example: 2 x 2 x 2 x 2 = 2^4
- Multiplying Indices — when multiplying indices with equal bases, add the powers. Example: 2^5 x 2^3 = 2^(5+3) = 2^8
- Dividing Indices — when dividing indices with equal bases, subtract the powers. Example: 2^5 / 2^3 = 2^(5-3) = 2^2
- Power of a Power — multiply the powers when raising a power to another power. Example: (2^3)^2 = 2^(3x2) = 2^6
- Negative Power — convert a negative power to positive by taking the reciprocal. Example: 2^-3 = 1/2^3
- Root — the inverse operation of a power, represented by the symbol √. Example: √4 = 2
- Law of Surds — the product of surds can be simplified by multiplying under the root. Example: √2 x √3 = √6
- Rationalising Surds — involves removing surds from the denominator of a fraction. Example: Rationalise 1/√2 by multiplying by √2/√2 to get √2/2
- Adding and Subtracting Surds — surds can only be added or subtracted if they have the same radicand. Example: √5 + 3√5 = 4√5
Exam Tips
Key Definitions to Remember
- Power: a number multiplied by itself several times
- Root: the inverse operation of a power
- Surd: an expression with a root symbol representing an irrational number
Common Confusions
- Forgetting to add powers when multiplying indices with the same base
- Trying to add or subtract surds with different radicands
Typical Exam Questions
- What is 2^3 x 2^4? Answer: 2^7
- Simplify √50. Answer: 5√2
- Rationalise the denominator of 1/√3. Answer: √3/3
What Examiners Usually Test
- Understanding and applying the rules of indices
- Simplifying expressions involving surds
- Rationalising the denominator in expressions with surds