MATHEMATICS ENCYCLOPEDIA

An arithmetic expression involving several numbers and multiple operations is not as easy as operations involving two numbers. BODMAS is used to solve the above expression. BODMAS is acronym for  B - Brackets O - Orders ( numbers involving powers and square roots ) D - Division M - Multiplication A - Addition S - Subtraction Start with brackets and follow the above rule from 1 to 6.

There are many expressions having square roots in their denominators. If the denominators are free from square roots then addition, substraction, multiplication and division will be more easy.  Rationalisation means the conversion of denominator into a rational number. You have to multiply both numerator and denominator by irrational number to make the denominator rational. The number multiplied is called rationalisation factor. 

Numbers that are not a root of any non-zero polynomial with integer or rational cofficient. All transcendental numbers are irrational but all irrationals are not transcendental. Transcendental numbers are the subset of irrational numbers. Examples include pi ( π ) and Euler's number (е ) etc. It is very difficult to show that a number is transcendental. It is not an algebriac number.

Oxford dictionary definition: The branch of mathematics dealing with the relations of the sides and angle of triangles and with the relevant functions of any angle. Cambridge dictionary definition: A type of mathematics that deals with the relationship between the angles and sides of triangle, used in measuring the height of buildings, mountains etc. The word 'trigonometry' is derived from Greek words 'tri' (meaning three), 'gon' (meaning sides) and 'metron' (meaning measure). The earliest known work on trigonometry was recorded in Egypt and Babylon. The values of trigonometric ratios of an angle do not vary with lengths of the sides of the triangle, if the angle remains the same.

When we say collection of objects is listed in a sequence, we usually mean that the collection is ordered in such a way that it has an identified first member, second member, third member and so on. The numbers occuring in a sequence are called its terms. The nth term is called the general term of the sequence. If a, b, c, d,......be in a sequence , then the expression a + b + c + d + ..........    is called the series associated with the given sequence. Sequences following specific patterns are called progressions.