Module 2 · Algebra
Chapter 23: Surds & Indices
Algebra
4 topics
What this chapter covers
The 4 topics below make up Surds & Indices on the CAT. Click any topic to open its notes, examples and practice test.
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Formula Reference Sheet
This chapter
Laws of indices
| Product of same base | a^m × a^n = a^(m+n) |
|---|---|
| Quotient of same base | a^m ÷ a^n = a^(m−n) |
| Power of a power | (a^m)^n = a^(m×n) |
| Power of a product / quotient | (ab)^n = a^n b^n; (a/b)^n = a^n / b^n |
| Zero and negative index | a^0 = 1; a^(−n) = 1 / a^n |
Surds & rationalization
| Fractional index = root | a^(m/n) = (ⁿ√a)^m = ⁿ√(a^m) |
|---|---|
| Product / quotient of roots | ⁿ√a × ⁿ√b = ⁿ√(ab); ⁿ√a ÷ ⁿ√b = ⁿ√(a/b) |
| Conjugate of (√a + √b) | √a − √b (their product = a − b) |
| Rationalize 1/(√a + √b) | (√a − √b) / (a − b) |
| Compound surd √(a ± 2√b) | √x ± √y where x + y = a, xy = b |
CAT reference
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