# 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 & 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 Rule an * am = am+n an * bn = (a*b)n Division Rule am/ 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 Rule n√(a)n= a n√(a)/b = n√(a) /n√(b) m√n√(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.