Simplification

BODMAS, surds, indices

221 practice questionsPage updated 27 Mar 2026Review metadata pendingPractice questions

Simplification is the process of reducing complex mathematical expressions to their simplest form. In competitive exams, simplification problems test your command over basic arithmetic operations, understanding of operator precedence (BODMAS), and ability to work with fractions, decimals, surds, and indices. These questions form the foundation of quantitative aptitude and require both speed and accuracy.

Key formulas and rules

BODMAS Rule: Brackets -> Orders (powers/roots) -> Division -> Multiplication -> Addition -> Subtraction

(a + b)^2 = a^2 + 2ab + b^2

(a - b)^2 = a^2 - 2ab + b^2

(a + b)(a - b) = a^2 - b^2

(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3

a^3 + b^3 = (a + b)(a^2 - ab + b^2)

a^3 - b^3 = (a - b)(a^2 + ab + b^2)

a^m x a^n = a^(m+n)

a^m / a^n = a^(m-n)

(a^m)^n = a^(mn)

a^0 = 1 (a != 0)

a^(-n) = 1/a^n

sqrta x sqrta = a

sqrt(a x b) = sqrta x sqrtb

sqrt(a/b) = sqrta/sqrtb

Rationalization: 1/(sqrta + sqrtb) = (sqrta - sqrtb)/(a - b)

Key concepts

BODMAS - Order of Operations

BODMAS dictates the sequence for simplifying expressions: B (Brackets - innermost first), O (Orders - powers and roots), D/M (Division and Multiplication - left to right), A/S (Addition and Subtraction - left to right). Common brackets types: () parentheses, {} braces, [] square brackets. Remember that division and multiplication have equal precedence, as do addition and subtraction. Always work left to right when precedence is equal.

Simplification

Key formulas and rules

Key concepts

BODMAS - Order of Operations

Fractions and Decimals

Surds (Irrational Roots)

Laws of Indices

Algebraic Identities in Simplification

Modulus and Absolute Value

Worked examples

Example 1

Example 2

Example 3

Example 4

Representative solved questions

Question 1

Question 2

Question 3

Common mistakes and useful habits

Ready to test your understanding?

Key formulas and rules

Key concepts

BODMAS - Order of Operations

Fractions and Decimals

Surds (Irrational Roots)

Laws of Indices

Algebraic Identities in Simplification

Modulus and Absolute Value

Worked examples

Example 1

Example 2

Example 3

Example 4

Representative solved questions

Question 1

Question 2

Question 3

Common mistakes and useful habits

Ready to test your understanding?

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