Formulas For Surds & Indices

Formulas For Surds and Indices

  • Surds: Surds are the natural numbers which can be expressed in the form \sqrt{p} + \sqrt{q}
  • Indices: Indices refers to the power to which a number is raised. For example; 3²
Formulas For Surds and Indices (2)

Formulas for Surds and Indices & Definitions

  • Surds: Numbers which can be expressed in the form \sqrt{p} + \sqrt{q} , where p and q are natural numbers and not perfect squares. 
  • For example : \sqrt{3}, it can’t be simplified.
    \sqrt{4}, it can be simplified so it is not a surds.
  • Indices: Indices refers to the power to which a number is raised. For example; 3²
  • Surds and Indices formulas pages is very useful for solving the ques.. Prepinsta provide Surds and Indices Formulas and ques.

Surds and Indices Formulas and Rule

Rule Name Rule
Multiplication Rulean * am = am+n
an * bn = (a*b)n
Division Ruleam/ an = am-n
an/ bn = (a/b)n
(an)m = an*m
n√(a)m = am/n
n√(a) = a 1/n
a-n = 1/an
Power Rulen√(a)n= a
n√(a)/b = n√(a) /n√(b)
mn√(a) = mn√(a)
a0 = 1

Basic Formula for Surds and Indices

  • (a + b)(a – b) = (a2 – b2)
  • (a + b)² = (a² + b² + 2ab)
  • (a – b)² = (a² + b²- 2ab)
  • (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
  • (a³ + b³) = (a + b)(a² – ab + b²)
  • (a³ – b³) = (a – b)(a²+ ab + b²)
  • (a³ + b³ + c³ – 3abc) = (a + b + c)(a² + b² + c² – ab – bc – ac)
  • When a + b + c = 0, then a³ + b³ + c³ = 3abc.

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