Formula : Surds & Indices

Surds & Indices: Surds: The irrational root of an integer. If you can't simplify a number to remove a square root (or cube root etc) then it is a surd.  Example: Number Simplifed As a Decimal Surd or not? √2 √2 1.4142135... Surd √3 √3 1.7320508... Surd √4 2 2 Not a surd √(1/4) 1/2 0.5 Not a surd Indices (  or Exponents ): Powers of numbers. They are defined as how many times a number multiplies by itself. Example:  The expression 25 is defined as follows: We call "2" the base and "5" the index. Laws of Indices: When m and n are positive integers,  am × an = am + n  am / an = am – n   (am)n = amn (ab)n = anbn (a/b)n = an / bn a0 = 1 Laws of Surds: When m and n are positive integers n√ a = a1/n n√ ab = n√ a * n√ b n√(a/b) = n√ a / n√ b  (n√ a)n = a m√n√ a = mn√ a (n√a)m = n√am Tips to simplify expressions with surds: In general Fractions in the form multiply top and bottom by Fractions in the form multiply the top and bottom by Fractions in the form multiply the top and bottom by   Note: For more examples: We will be using these formula in later sessions and will refer back here.