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यह Simplification प्रश्न “सरल करके मान ज्ञात कीजिए: 48^2 - 52^2।” के लिए सही interpretation और stepwise calculation विकसित करता है। Explanation मूल mathematical conditions सुरक्षित रखकर -400 की पुष्टि करता है तथा signs, brackets, operation order, factors, remainder और fractions से जुड़ी सामान्य गलतियाँ स्पष्ट करता है।
सत्यापित उत्तर -400 है और सही विकल्प B है। “सरल करके मान ज्ञात कीजिए: 48^2 - 52^2।” को हल करते समय calculation शुरू करने से पहले सभी चिन्ह, brackets, powers और संख्यात्मक शर्तें ठीक रखें। प्रश्न के साथ उपलब्ध विशिष्ट गणना है: 48^2 - 52^2 पर BODMAS लगाने से -400 प्राप्त होता है।। अन्य विकल्प -340, -380, -360 BODMAS बदलने, negative sign गलत लेने, reciprocal गलत लगाने, divisibility condition छोड़ने या exact value को जल्दी round करने से मिल सकते हैं।
FAQ
Common questions and clear answers for this topic.
Simplification involves solving mathematical expressions using BODMAS rule. BODMAS stands for: Brackets, Orders (powers and roots), Division, Multiplication, Addition, Subtraction. The rule determines the order in which operations are performed. Simplification is a major topic in SSC CGL Tier 1, IBPS Clerk, SBI Clerk, Railway Group D, and all competitive exams.
Important properties for Simplification: Squares up to 30, Cubes up to 15, Square roots of perfect squares up to 400, Multiplication tables up to 20. Also remember: a squared - b squared = (a+b)(a-b), (a+b) squared = a squared + 2ab + b squared, (a-b) squared = a squared - 2ab + b squared, a cubed + b cubed = (a+b)(a squared - ab + b squared). Memorizing these speeds up simplification in exams.
Approximation means finding a value close to the exact answer. In simplification and DI questions, when options are far apart, use rounding to save time. Techniques: Round to nearest 10 or 100, use percentage fractions (25% = 1/4, 33% = 1/3), estimate square roots. In competitive exams, approximation questions require finding the value closest to the actual answer.
Fraction simplification shortcuts: When adding fractions a/b + c/d, use cross multiplication: (ad+bc)/bd. Simplify by finding GCD first. Useful fraction equivalents: 1/7 = 0.142, 1/6 = 0.167, 1/3 = 0.333, 2/3 = 0.667. For mixed numbers: 3 and 2/5 = 17/5. When dividing fractions: multiply by reciprocal. Practice minimum 20 simplification questions daily for exam preparation.
Surds are irrational numbers expressed with square roots or other roots. Simplification rules: root(a) x root(b) = root(ab), root(a)/root(b) = root(a/b), (root(a)) squared = a. Rationalization: Multiply top and bottom by conjugate to remove surd from denominator. Example: 1/(2+root 3) = (2-root 3)/((2+root 3)(2-root 3)) = (2-root 3)/(4-3) = 2-root 3. Surds appear in SSC CGL and IBPS exams.
