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:
a² - b², (a+b)², (a-b)²Approximation 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.
BODMAS stands for:
(), then [], then {})aⁿ and roots √a)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.
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.
These three identities appear in SBI Clerk more often than people expect:
a² - b² = (a + b)(a - b)(a + b)² = a² + 2ab + b²(a - b)² = a² - 2ab + b²For 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.
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.
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.
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.
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.
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.
For any √n where n is close to a perfect square, anchor to the nearest perfect square. √(n) ≈ √(k²) where k² 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.
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.
When you see a simplification question in the exam hall, run this decision tree in under 3 seconds:
Step 1 — Identify the type:
√ or aⁿ? → Resolve all surds and powers first, then handle operators.a² - b² or similar patterns? → Apply algebraic identity before computing.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.
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.
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.
Solving path: √169 — anchor to perfect squares near 169. 13² = 169, so √169 = 13. √121 — 11² = 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.
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.
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 ÷.
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.
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.
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.
Solving path: 20% of 150 = (1/5) × 150 = 30. 30% of 100 = 30. Total: 30 + 30 = 60.
Treating multiplication as higher priority than division. They are equal. 12 ÷ 4 × 3 is (12 ÷ 4) × 3 = 9, not 12 ÷ 12 = 1. This error alone causes wrong answers in one out of every three BODMAS questions attempted without proper training.
Resolving brackets in the wrong order. When you have nested brackets — say {2 × [3 + (4 - 1)]} — work from the innermost () outward. Candidates who work [] before () get a different (wrong) intermediate value and then carry the error forward.
Adding square roots before simplifying. √4 + √9 is NOT √(4+9) = √13. You must compute 2 + 3 = 5. The root does not distribute over addition. This is among the most commonly penalised errors in surd questions.
Computing a² - b² by squaring both terms separately. This works but costs 10+ extra seconds. At the pace SBI Clerk demands, that difference is measurable across a set of 10 questions.
Ignoring parity as an eliminator. If your computed answer is odd and three of the four options are even, you have almost certainly made an error. Use parity to self-check before moving on — it takes 1 second and can save you from marking the wrong answer.
Using long multiplication for percentage × number when a fraction equivalent exists. Every time you write (20/100) × 150 and multiply out, you are using 3-4 unnecessary steps. The fraction 1/5 × 150 = 30 is a single mental division. Over a full set of percentage simplification questions, this habit difference can amount to 2-3 minutes — enough to attempt several additional questions.