Simplification, BODMAS & Surds
Practice 290+ SSC CGL Simplification & Surds PYQs online. Master VBODMAS rules, surd rationalization, continuous fractions & step-by-step solutions.
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๐ฏ High-Yield Syllabus Breakdown
These high-frequency concepts account for over 90% of all questions asked in Simplification, BODMAS & Surds:
- V-BODMAS Rule (Vinculum, Bracket, Of, Division, Multiplication, Addition, Subtraction)
- Rationalization of Quadratic Surds
- Continued Fractions (Ladder Fractions) Short Method
- Square Roots of Surds: โ(a ยฑ 2โb)
- Decimal Fractions & Recurring Decimals (0.pฬ = p/9, 0.pqฬ = (pq - p)/90)
โก Essential Formulas & Speed Shortcuts
Formulas and time-saving shortcuts to solve Simplification questions in under 45 seconds:
Square root of a ยฑ 2โb: Find two numbers x and y such that x + y = a and xยทy = b; result is โx ยฑ โy.
Recurring Decimals: 0.abcฬ = (abc - a) / 990.
Always evaluate "OF" before division in BODMAS.
๐ Sample Solved Exam Questions
Preview authentic questions from this chapter with full step-by-step solutions:
๐ก View Step-by-Step Solution & Answer
Correct Answer: 1 8
- Step 1: Understand problem conditions and equations.
- Step 2: W e have, 4 5 1 1 3 1 2 1 4 4 5 1 1 3 1 9 4 4 5 1 1 3 4 9 4 5 1 9/31 4/31 5/40 160 โ + + + =โ + + =โ + + =โ + =โ ร = โ โ ==155/40 5/40 1 8
- Step 3: Evaluating gives verified answer: 1 8.
โก Speed Tip: Verify intermediate calculations and units.
๐ก View Step-by-Step Solution & Answer
Correct Answer: 20/101
- Step 1: Understand problem conditions and equations.
- Step 2: Assume that, a =+ + =+ =+ =1 1/10 1/10 1 1/101 10 1/10 101/111 101 and b =โ + =โ =โ =1 1/10 1/10 1 1/101 10 1/10 101/91 101 Now, Given expression = aa bb abรโ ร[] รท ab ab ab ab ab 22/111 101/91 101/111 101/91 101 1 โ = โ() +() = โ + 1/11 101/91 101/20 101/202 101/111 101/91 101/20 202/111 91/4040 101 ร = ร ร = ร ร = 0/01
- Step 3: Evaluating gives verified answer: 20/101.
โก Speed Tip: Verify intermediate calculations and units.
๐ก View Step-by-Step Solution & Answer
Correct Answer: 56/53
- Step 1: Understand problem conditions and equations.
- Step 2: W e have, 4 1 7 2 1 7/31 2/11 7 1 2 1 2 1 5 1 5/29 7/15 7 7 2 8 7 1 2 1 2 5/24 14 7/49 16 โ + รท + + โ = โ + รท + + = + 1/14 1 2/24 53 2/65 14/53 106/24 28/65 130/53 56/53 รท + =รท + =ร =
- Step 3: Evaluating gives verified answer: 56/53.
โก Speed Tip: Verify intermediate calculations and units.
โ Frequently Asked Questions (FAQs)
How to simplify โ(7 + 2โ10)?
Find two numbers with sum 7 and product 10: they are 5 and 2. Therefore, โ(7 + 2โ10) = โ5 + โ2.