What is 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19?

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.