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
Formulas For Surds and Indices (2)

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 NameSurds RuleIndices Rule
Multiplication Rulean * bn = (a*b)nan * am = a(m+n)
Division Rulean/ bn = (a/b)nam / an = a(m-n)
Power Rule

(an)m = (a)nm
n√a = a(1/n)

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.

Prime Course Trailer

Related Banners

Get PrepInsta Prime & get Access to all 200+ courses offered by PrepInsta in One Subscription

Get over 200+ course One Subscription

Courses like AI/ML, Cloud Computing, Ethical Hacking, C, C++, Java, Python, DSA (All Languages), Competitive Coding (All Languages), TCS, Infosys, Wipro, Amazon, DBMS, SQL and others

Checkout list of all the video courses in PrepInsta Prime Subscription

Checkout list of all the video courses in PrepInsta Prime Subscription