Simplification

medium importance~2 Q in Tier 126 formulas⚡ 14 shortcuts5 subtopics

Overview Learn (5)Formulas (26)Examples (5)Practice (65)

BODMAS, identity-based fractions, surds and indices, square/cube roots and approximation. These are the fastest marks in Tier 1 — usually 1–2 questions per shift — and the same skills (identities, surd handling) power the algebra questions.

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Learn — 5 subtopics

One page per subtopic: detailed notes, every question type, formulas, tricks and practice sets.

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Formula sheet

Every formula on one printable page, grouped by subtopic.

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Solved examples

5 exam-level questions worked step by step.

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Practice & test

65 questions — untimed practice or a timed test with analysis.

Track record in the exam

avg 1.0 Q / shift2024: 1–2 Q2025: 1 Q

Questions per shift in recent SSC CGL papers.

Test difficulty mix (65 questions)

23 easy34 medium8 hard

Question patterns exams keep repeating

Taken from previous-year papers. If a pattern is marked "very common", expect to see it in your exam.

VBODMAS with 'of' and brackets

very common

Spot it:

A long mixed expression with ÷, ×, 'of', brackets and a vinculum. The word 'of' is the trap marker.

How to solve: Follow VBODMAS strictly: vinculum, brackets innermost first, then 'of' (it multiplies but comes before ÷ and ×), then ÷ and × left to right, then + and −. A minus before a bracket flips every sign inside.

Example: Evaluate $64 \div 4 \text{ of } 2 + 8 \times 3$ .

'of' first: $64 \div 8 = 8$ , then $+ 24 = 32$ .

Learn this in “BODMAS, 'of', brackets & vinculum” →

Identity fractions: (a³±b³) over the quadratic

very common

Spot it:

A fraction whose top is a sum/difference of cubes (often decimals) and whose bottom is a²∓ab+b² or a²±ab+b².

How to solve: Match the denominator to the identity factor and cancel: (a³+b³)/(a²−ab+b²) = a+b; (a³−b³)/(a²+ab+b²) = a−b. Read the middle sign carefully — minus below pairs with plus above.

Example: $\frac{(15.2)^3-(5.2)^3}{(15.2)^2+15.2\times5.2+(5.2)^2}$ = ?

Denominator a²+ab+b² → value = a − b = 10.

Learn this in “Algebraic identities in numerical simplification” →

x + 1/x family

very common

Spot it:

'If $x + \frac{1}{x} = 4$ , find $x^2 + \frac{1}{x^2}$ (or $x^3 + \frac{1}{x^3}$ , $x^4 + \frac{1}{x^4}$ )' — also the minus version.

How to solve: Square the given: $x^2 + \frac{1}{x^2} = k^2 - 2$ (plus) or $k^2 + 2$ (minus). Cube: $k^3 \mp 3k$ . Fourth power: square the squared result and subtract 2.

Example: $x+\frac1x=4$ → $x^3+\frac{1}{x^3}$ ?

$4^3 - 3 \times 4 = 52$ .

Learn this in “Algebraic identities in numerical simplification” →

Indices equation with a common base

very common

Spot it:

An equation like $2^{x+3} \times 4^{x-1} = 128$ or $3^{x+2} + 3^x = 810$ .

How to solve: Write every term as a power of one prime (4 = 2², 25 = 5²). Take the common power outside if it is a sum. Then equate the exponents.

Example: Solve $2^{x+3} \times 4^{x-1} = 128$ .

$2^{3x+1} = 2^7$ → $x = 2$ .

Learn this in “Surds & indices” →

Rationalisation and surd sums

very common

Spot it:

Fractions like $\frac{1}{\sqrt7-\sqrt6}$ , sums of conjugate fractions, or a surd plus its reciprocal.

How to solve: Multiply top and bottom by the conjugate. Telescoping chains collapse to (first root − last root). If x = a+2√b type, then 1/x is the conjugate a−2√b.

Example: $\frac{1}{\sqrt9+\sqrt8}+\dots+\frac{1}{\sqrt2+1}$ = ?

Each term is $\sqrt k - \sqrt{k-1}$ ; the sum collapses to $3 - 1 = 2$ .

Learn this in “Surds & indices” →

Root of a surd: √(a + 2√b)

common

Spot it:

Expressions like $\sqrt{11+6\sqrt2}$ or $\sqrt{7+4\sqrt3}$ (and the two-root sum/difference versions).

How to solve: Rewrite as $\sqrt{a+2\sqrt b}$ ; split $a = x+y$ with $xy = b$ ; the value is $\sqrt x+\sqrt y$ . For a pair like $\sqrt{7+4\sqrt3} \pm \sqrt{7-4\sqrt3}$ , take $x = 2+\sqrt3$ , $y = 2-\sqrt3$ and add or subtract.

Example: $\sqrt{11+6\sqrt2}$ = ?

$11 = 9+2$ , $9 \times 2 = 18$ → $3+\sqrt2$ .

Learn this in “Surds & indices” →

Cube and square roots of perfect powers; least number for a square

very common

Spot it:

'Find ∛9261', '√11025', or 'least number to add/subtract to N to make a perfect square'.

How to solve: Cube root: group digits in threes, use the unit-digit swap map (2↔8, 3↔7) plus a size check. Square root: digit pairs, last-digit map and neighbours. For least add/subtract, bracket N between k² and (k+1)².

Example: Least number to add to 1300 for a perfect square?

$37^2 = 1369$ → add $69$ .

Learn this in “Square roots & cube roots” →

Infinite and nested radicals

common

Spot it:

$\sqrt{6+\sqrt{6+\dots}}$ , $\sqrt{20\times\sqrt{20\times\dots}}$ , or a finite nest like $\sqrt{30+\sqrt{24+\sqrt{144}}}$ . (already exists as solved example — same type, new numbers)

How to solve: Infinite plus-radical: solve $x^2 = a + x$ (or use $a = k(k+1)$ → answer $k+1$ ). Infinite product-radical: the answer is $a$ . Finite nests: work from the innermost root outward.

Example: $\sqrt{20\times\sqrt{20\times\sqrt{20\times\cdots}}}$ = ?

$x^2 = 20x$ → $x = 20$ .

Learn this in “Square roots & cube roots” →

Approximation with percentages, products and roots

very common

Spot it:

'What approximate value comes in place of ?' with decimals like 1199.8, 24.98%, √2303.9.

How to solve: Round every number to a friendly value (nearest ten, percentage → fraction, root → nearest perfect power), compute mentally, and pick the closest option. Options are spaced far apart; do not chase exact decimals.

Example: $29.9\%$ of $1199.8 + 15.02 \times 23.9 ≈$ ?

$360 + 360 = 720$ .

Learn this in “Approximation” →

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