surds & indices

If K is not a perfect nth power of any number, then is called a surd of the n t h order. A surd is always an irrational numbe..

If K is not a perfect nth power of any number, then is called a surd of the n t h order. e.g., is a surd of the third order. is a surd of the second order. A surd is always an irrational numb..

An irrational root of a positive rational number is called a surd. Consider a number with base 'a' as a positive rational number with power of a fraction, say then Since is an n t h root, it is called a surd of order n, if it is irrational. e.g., (i) is a surd..

is the conjugate surd of . Their product is a rational number, In the above example (6), and are conjugate surds of each oth..

A rational number is a number of the form where p and q are integers and . Problems involving rational numbers are simplified using 'BODMAS' rule. A rational number can be represented in the decimal form. When a rational number is represented as a decimal, it will be either a terminat..

Laws of Indices: If m and n are positive integers, and then (i) a m a n = a m + n [Product Law] (ii) [Quotient Law] Surd: An irrational root of a positive rational number is called a surd..

We know that 64 = 2 x 2 x 2 x 2 x 2 x 2 = 2 6 Here 2 is called the base and 6 is called the power (or index or exponent). We say that "64 is equal to base 2 raised to the power 6". The Laws of Indices are : Product Law, Quotient Law, Power Law, (ab) m = a m . b m . An irrational root of a ..

If m is a positive integer, a x a x a . m times is written as a m . a is called the base and m is the power. We read it as "a raised to the power m". The power is also called "the index" or "the exponent". When the power or index is a fraction say then and it is a surd of order n. In this..

Indices - If m is a positive integer, a x a x a .. m times is written as am. a is called the base and m is the power. We read it as "a raised to the power m". The power is also called "the index" or "the exponent". When the power or index is a fraction say then and it is a surd of order n..

Question: Calculate the distance between the points (-3, 5) and (4, -6), leave your answer in surd form. [2 Mark] Answer: Let A(-3, 5) and B(4, -6) ..