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Formulas For Surds & Indices
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


More about 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 Rule
Rule Name | Surds Rule | Indices Rule |
---|---|---|
Multiplication Rule | an * bn = (a*b)n | an * am = a(m+n) |
Division Rule | an/ bn = (a/b)n | am / an = a(m-n) |
Power Rule | (an)m = (a)nm | a(nm)) = anm 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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- HCF and LCM – Questions Formulas | How to Solve Quickly | Tricks & Shortcuts
- Number System – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
- Number Decimals & Fractions – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
- Divisibility – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
- Ages – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
- LCM – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
- HCF – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
- Inverse – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
- HCF and LCM –
Questions
Formulas |
How to Solve Quickly |
Tricks & Shortcuts - Number System –
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Formulas |
How to Solve Quickly |
Tricks & Shortcuts - Number Decimals & Fractions –
Questions |
Formulas |
How to Solve Quickly |
Tricks & Shortcuts - Divisibility –
Questions |
Formulas |
How to Solve Quickly |
Tricks & Shortcuts - Ages –
Questions |
Formulas |
How to Solve Quickly |
Tricks & Shortcuts
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