# 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 √p + √q , where p and q are natural numbers and not perfect squares. Irrational numbers which contain the radical sign (n√) are called as surds Hence, the numbers in the form of √3, 3√2, ……. n√x in other words
• 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.

### Types of Surds and Definitions

• Pure Surds:- Those surds which do not have factors other than 1. For example 2√3, 3√7
• Mixed Surds:- Those surds which do not have a factor of 1. For example √27 = 3√3, √50 = 5√2
• Similar Surds:- When the radicands of two surds are the same. For example 5√2 and 7√2
• Unlike Surds:- When the radicands are different. For example √2 and 2√5

## Surds and Indices Formulas and Rule

Rule NameSurds RuleIndices Rule
Multiplication Rulea^n * b^n = (a*b)^na^n * a^m = a^(m+n)
Division Rulea^n/ b^n = (a/b)^n
(a^n)^m = [a^(n)^m]
n√a = a^(1/n)
a^m / a^n = a^(m – n)
(p^n)^m = p^(n-m)
p^(-n) = 1/(p^n)
Power Rule

n√(a)n = a
n√(a)/b = n√(a)/n√(b)
m√n√(b) = mn√(b)

a^0 = 1
[a/b]^n = (a^n)/(b^n)
(ab)^n = a^n x b^n

## 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.