Simplification & Approximation for SBI Clerk — BODMAS, Surds, and Indices

beginner 18 min read

Concept

Simplification is the process of reducing a mathematical expression to its most compact numerical form using a fixed order of operations. Approximation is a related skill — you round values strategically to get close enough to the answer without exact calculation.

Here is the analogy that makes this stick: think of a complex expression as a recipe with a strict sequence of steps. You do not add flour before cracking eggs just because flour appears earlier in the ingredient list. Similarly, in mathematics, you follow BODMAS — Brackets, Orders (powers and roots), Division, Multiplication, Addition, Subtraction — in that exact sequence regardless of how the expression is written left to right.

Why does SBI Clerk test this so heavily? Because simplification is a proxy for speed and accuracy under pressure. A candidate who has internalised BODMAS and can spot shortcuts in surd problems, percentage calculations, and algebraic identities will consistently gain 30-40 seconds per question over someone doing brute computation. Those seconds compound across the paper.

The typical simplification question in SBI Clerk falls into one of four buckets:

  1. Pure BODMAS — a single expression mixing all four operations, possibly with brackets
  2. Surds and indices — square roots, cube roots, and powers that simplify to clean integers
  3. Percentage-based — "x% of a + y% of b" expressions that reduce quickly with fraction equivalents
  4. Difference of squares / algebraic identitiesa² - b², (a+b)², (a-b)²

Approximation questions are a softer version: the answer choices are spaced far enough apart that you only need to be within 2-5% of the exact value. The skill there is knowing when to round up, when to round down, and how to pick the direction that keeps your error small.

You do not need calculus. You do not need logarithm tables. You need a clean mental hierarchy, a dozen memorised values (squares up to 30, cubes up to 15, square roots of perfect squares up to 200), and the discipline to apply the right shortcut to the right problem type.


Deep Dive

BODMAS — The Non-Negotiable Hierarchy

BODMAS stands for:

A critical nuance: Division and Multiplication have equal precedence. When both appear in the same expression without brackets, work left to right. Same rule applies to Addition and Subtraction.

Look — the most common wrong answer in a BODMAS question comes from treating multiplication as strictly higher than division. It is not. They are equal. 24 ÷ 3 × 2 is (24 ÷ 3) × 2 = 8 × 2 = 16, not 24 ÷ (3 × 2) = 4.

Working through a multi-operation expression:

Take 16 + 24 ÷ 3 × 2. Step 1 — no brackets, no orders. Step 2 — Division and Multiplication, left to right: 24 ÷ 3 = 8, then 8 × 2 = 16. Step 3 — Addition: 16 + 16 = 32.

Surds — Know Your Perfect Squares and Cubes Cold

A surd is an expression involving an irrational root that cannot be simplified to a whole number. But in SBI Clerk, surds almost always simplify to whole numbers. That is the trick — the paper is designed to test whether you recognise perfect squares, not whether you can handle irrational numbers.

Memorise these:

| √n | n | |------|-----| | 11 | 121 | | 12 | 144 | | 13 | 169 | | 14 | 196 | | 15 | 225 |

For combined surd expressions like √64 × √36 ÷ √16, apply BODMAS after finding each root: 8 × 6 ÷ 4 = 48 ÷ 4 = 12. Do not multiply under the root first — resolve each surd independently, then apply the operator.

Algebraic Identities — The Speed Multipliers

These three identities appear in SBI Clerk more often than people expect:

For 15² - 13²: applying (15+13)(15-13) = 28 × 2 = 56 takes 4 seconds. Computing 225 - 169 = 56 takes 8 seconds. Same answer, double the time.

Percentages as Fractions — The Real Speed Hack

Stop computing (x/100) × N every time. Convert common percentages to fractions once and burn them into memory:

| Percentage | Fraction | |-----------|----------| | 10% | 1/10 | | 20% | 1/5 | | 25% | 1/4 | | 33.33% | 1/3 | | 50% | 1/2 | | 75% | 3/4 |

So 25% of 240 = 240 ÷ 4 = 60. No multiplication, no division by 100.

For combined expressions like 20% of 150 + 30% of 100: (1/5) × 150 + (30/100) × 100 = 30 + 30 = 60. That is two mental arithmetic steps, total.

Approximation Strategy

When the question says "approximately" or the answer options have gaps of 5+ units, round to the nearest "friendly" number. Rules:

For instance, √(399) — recognise that 20² = 400, so √399 ≈ 20. The exact value is 19.97. For any SBI Clerk option set, 20 is close enough.


Memory Tricks & Shortcuts

patternLeft-to-Right Lock for D and M

When you see Division and Multiplication side by side without brackets, draw an invisible arrow pointing left to right. Never look at M before D if D appears first. Example: 63 ÷ 9 × 4 — the arrow says do 63 ÷ 9 = 7 first, then 7 × 4 = 28. Wrong approach: 9 × 4 = 36, 63 ÷ 36 — fractional disaster. Standard confusion-prone path: 8-10 seconds of hesitation. With the arrow trick: immediate, 2 seconds.

patternDifference of Squares Radar

Whenever you see two squared terms being subtracted — a² - b² — do not compute each square. Immediately factor: (a+b)(a-b). For 15² - 13²: (28)(2) = 56. Step count with direct computation: subtract 225 from 169 = 5 steps. Step count with identity: add 15+13, subtract 15-13, multiply = 3 steps. Saves 6-8 seconds per question.

substitutionPercent-to-Fraction Flash

When the percentage is 10%, 20%, 25%, or 50%, never write (x/100) ×. Substitute the fraction directly: 25% → ÷4, 20% → ÷5, 50% → ÷2, 10% → ÷10. For 25% of 240: write 240 ÷ 4 = 60 in your head. Standard method: (25 × 240) ÷ 100 = 6000 ÷ 100 = 3 written steps, ~12 seconds. Fraction substitution: 1 mental step, ~4 seconds.

estimationPerfect Square Anchoring for Surds

For any √n where n is close to a perfect square, anchor to the nearest perfect square. √(n) ≈ √(k²) where is the nearest perfect square. For approximation questions, this gives you the answer in one glance. √170 ≈ √169 = 13. √148 ≈ √144 = 12. This avoids all calculation. Standard long-division method for square roots: 45+ seconds. Anchor method: 3 seconds.

patternBracket-First, Always

Before scanning the rest of an expression, circle all brackets mentally and resolve them top-down (innermost first). Even if multiplication appears outside the bracket and looks urgent, the bracket comes first. This single habit eliminates the two most common BODMAS errors. Practice on any expression: bracket content becomes one number, then you apply BODMAS to the remaining flat expression. Reduces multi-step BODMAS questions from 5-step to 3-step processing.


Fast-Solving Framework

When you see a simplification question in the exam hall, run this decision tree in under 3 seconds:

Step 1 — Identify the type:

Step 2 — Simplify in priority order: Brackets → Orders → D/M left-to-right → A/S left-to-right

Step 3 — If it is an approximation question: Check the gap between answer options. If options differ by more than 5 units, round aggressively. If options are close (within 2-3 units), be more precise.

Step 4 — Eliminate if stuck: In most SBI Clerk simplification questions, two of the four options are clearly wrong by parity (even vs odd) or by order of magnitude. Eliminate them first, then compute between the remaining two. This saves recalculation.

Target time: 20-30 seconds for pure BODMAS, 15-20 seconds for surd or percentage questions where you know your values cold.


Solved PYQs

Why this question: Tests whether you apply D/M before A/S, and whether you handle left-to-right order correctly for D and M.

Previous Year Questionपिछले वर्ष का प्रश्न
What is the value of 12 + 8 × 3 - 6 ÷ 2?
12 + 8 × 3 - 6 ÷ 2 का मान क्या है?
  1. 33
  2. 63
  3. 30
  4. 24
  1. 33
  2. 63
  3. 30
  4. 24
Solutionसमाधान
Following BODMAS rule: First division and multiplication from left to right: 8 × 3 = 24, 6 ÷ 2 = 3. Then addition and subtraction from left to right: 12 + 24 - 3 = 33.
BODMAS नियम का पालन करते हुए: पहले भाग और गुणा बाएं से दाएं: 8 × 3 = 24, 6 ÷ 2 = 3। फिर जोड़ और घटाव बाएं से दाएं: 12 + 24 - 3 = 33।

Solving path: Scan for brackets — none. Scan for orders — none. Identify D/M positions: 8 × 3 and 6 ÷ 2. Left to right: 8 × 3 = 24, then 6 ÷ 2 = 3. Now the expression is 12 + 24 - 3. Left to right: 12 + 24 = 36, 36 - 3 = 33. Done.


Why this question: Tests perfect square recognition. If you have not memorised 13² = 169 and 11² = 121, this takes 30+ seconds. If you have, it takes 5.

Previous Year Questionपिछले वर्ष का प्रश्न
What is the value of √169 + √121?
√169 + √121 का मान क्या है?
  1. 24
  2. 22
  3. 20
  4. 26
  1. 24
  2. 22
  3. 20
  4. 26
Solutionसमाधान
√169 = 13 and √121 = 11. Therefore, √169 + √121 = 13 + 11 = 24.
√169 = 13 और √121 = 11। इसलिए, √169 + √121 = 13 + 11 = 24।

Solving path: √169 — anchor to perfect squares near 169. 13² = 169, so √169 = 13. √12111² = 121, so √121 = 11. Sum: 13 + 11 = 24.


Why this question: Classic percentage shortcut test. If you write out (25/100) × 240 you are wasting time the paper does not give you.

Previous Year Questionपिछले वर्ष का प्रश्न
What is 25% of 240?
240 का 25% कितना होगा?
  1. 60
  2. 50
  3. 70
  4. 65
  1. 60
  2. 50
  3. 70
  4. 65
Solutionसमाधान
25% of 240 = (25/100) × 240 = 240 ÷ 4 = 60.
240 का 25% = (25/100) × 240 = 240 ÷ 4 = 60।

Solving path: Recognise 25% = 1/4. 240 ÷ 4 = 60. One mental step.


Why this question: Tests left-to-right rule for D/M. The trap is computing 3 × 2 = 6 first, then 24 ÷ 6 = 4, giving 16 + 4 = 20 — which is not among the options, but the anxiety of seeing a wrong answer can cause a recomputation spiral.

Previous Year Questionपिछले वर्ष का प्रश्न
What is the value of 16 + 24 ÷ 3 × 2?
16 + 24 ÷ 3 × 2 का मान क्या है?
  1. 32
  2. 26
  3. 30
  4. 28
  1. 32
  2. 26
  3. 30
  4. 28
Solutionसमाधान
Following BODMAS: First 24 ÷ 3 = 8, then 8 × 2 = 16. Finally, 16 + 16 = 32.
BODMAS के अनुसार: पहले 24 ÷ 3 = 8, फिर 8 × 2 = 16। अंत में, 16 + 16 = 32।

Solving path: Left to right for D/M: 24 ÷ 3 = 8 first, then 8 × 2 = 16. Addition: 16 + 16 = 32.


Why this question: Tests whether you resolve each surd independently before applying operators, and then whether you apply left-to-right rule for × and ÷.

Previous Year Questionपिछले वर्ष का प्रश्न
Simplify: √64 × √36 ÷ √16
सरल कीजिए: √64 × √36 ÷ √16
  1. 12
  2. 8
  3. 16
  4. 10
  1. 12
  2. 8
  3. 16
  4. 10
Solutionसमाधान
√64 = 8, √36 = 6, √16 = 4. Therefore: 8 × 6 ÷ 4 = 48 ÷ 4 = 12.
√64 = 8, √36 = 6, √16 = 4। इसलिए: 8 × 6 ÷ 4 = 48 ÷ 4 = 12।

Solving path: Resolve surds: √64 = 8, √36 = 6, √16 = 4. Expression becomes 8 × 6 ÷ 4. Left to right: 8 × 6 = 48, then 48 ÷ 4 = 12.


Why this question: Classic a² - b² identity trap. The paper expects you to know the shortcut.

Previous Year Questionपिछले वर्ष का प्रश्न
Find the value of 15² - 13²
15² - 13² का मान ज्ञात कीजिए।
  1. 56
  2. 62
  3. 58
  4. 54
  1. 56
  2. 62
  3. 58
  4. 54
Solutionसमाधान
Using the formula a² - b² = (a+b)(a-b): 15² - 13² = (15+13)(15-13) = 28 × 2 = 56.
सूत्र a² - b² = (a+b)(a-b) का उपयोग करके: 15² - 13² = (15+13)(15-13) = 28 × 2 = 56।

Solving path: Apply (a+b)(a-b): (15+13)(15-13) = 28 × 2 = 56. Two multiplications, no squaring required.


Why this question: Straightforward BODMAS but the left-to-right D/M rule is again the point of failure for unprepared candidates.

Previous Year Questionपिछले वर्ष का प्रश्न
Simplify: 63 ÷ 9 × 4 + 18
सरल कीजिए: 63 ÷ 9 × 4 + 18
  1. 46
  2. 42
  3. 48
  4. 40
  1. 46
  2. 42
  3. 48
  4. 40
Solutionसमाधान
Following BODMAS from left to right: 63 ÷ 9 = 7, then 7 × 4 = 28. Finally, 28 + 18 = 46.
BODMAS बाएं से दाएं के अनुसार: 63 ÷ 9 = 7, फिर 7 × 4 = 28। अंत में, 28 + 18 = 46।

Solving path: 63 ÷ 9 = 7, then 7 × 4 = 28. Addition: 28 + 18 = 46.


Why this question: Tests combined percentage computation. The shortcut is fraction conversion for both terms.

Previous Year Questionपिछले वर्ष का प्रश्न
Find 20% of 150 + 30% of 100
150 का 20% + 100 का 30% ज्ञात कीजिए।
  1. 60
  2. 50
  3. 70
  4. 65
  1. 60
  2. 50
  3. 70
  4. 65
Solutionसमाधान
20% of 150 = (20/100) × 150 = 30. 30% of 100 = (30/100) × 100 = 30. Total = 30 + 30 = 60.
150 का 20% = (20/100) × 150 = 30। 100 का 30% = (30/100) × 100 = 30। कुल = 30 + 30 = 60।

Solving path: 20% of 150 = (1/5) × 150 = 30. 30% of 100 = 30. Total: 30 + 30 = 60.


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