Formulas For Surds & Indices

May 28, 2023

Formulas For Surds and Indices

Go through the entire page to know important formulas for Surds and Indices to solve objective Surds and Indices quickly.

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

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 Rule

Rule Name	Surds Rule	Indices Rule
Multiplication Rule	aⁿ * bⁿ = (a*b)ⁿ	aⁿ * a^m = a^(m+n)
Division Rule	aⁿ/ bⁿ = (a/b)ⁿ	a^m / aⁿ = a^(m-n)
Power Rule	(aⁿ)^m = (a)^nmn√a = a^(1/n)	a^{(n^m)}) = a^{n^m} a^-n = 1/(aⁿ)

Surds and Indices basic Formula

(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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