How to do Division of Radicals

Introduction:
                  Radical numbers are in the form of square root. The square root present in the radical number may be either a cubic root or square root. The radical number is present inside each square root or cubic root. The index number is present outside the each square root or cubic root. For example, `root(3)(4)` is known as the radicals.

Example for How to do Division of Radicals

Example 1: How to divide the following radicals, `1/(sqrt(5) - sqrt(6))` .
Solution:
Step 1: Write the given radicals for division, we get,

`1/(sqrt(5) - sqrt(6))`

Step 2: The next step, for performing division , we have to take the conjugate. That means, the denominator term is taken and the sign of the denominator is changed. Then we have multiply the given radicals in both the numerator and denominator.

`1/(sqrt(5) - sqrt(6))`  `xx`  `(sqrt(5) + sqrt(6))/(sqrt(5) + sqrt(6))`

Step 3: By simplifying the above expression, we get,

`(sqrt(5) + sqrt(6))/(sqrt(5)^2 - sqrt(6)^2)`

`(sqrt(5) + sqrt(6))/(5 - 6)`

`(sqrt(5) + sqrt(6))/ - 1`

= - (  `sqrt(5) + sqrt(6)` )

       = - `sqrt(5)`  - `sqrt(6)`
This is the required solution for the division of radicals.

Explain Trigonometry Angles

Introduction:   

  Trigonometry is that branch of mathematics which deals with the measurement of sides and angles of triangles and to similar triangles. 
Angles:

     An angle is an amount of rotation of a half-line (or ray) in a plane about its end point from an initial position to a terminal position. The important terms are: Measurement of angle, Positive and Negative angles, Lines at right angles, Quadrants, Angle in standard position. 

Measurement of Angles:
     To measure an angle we shall use two kinds of units, the degree unit and the radian unit.
     A degree(Sexagesimal system) is defined to be an angle formed by half-line (or a ray) rotated about its end point (1/360) of a complete revolution.
     Types of Angles: Acute angle, Obtuse angle, Right angle, Reflex angle, A straight angle. 
Radian Measure(Circular System)
     A radian is the measuring angles at the centre of a circle subtended by an arc, whose arc length and arc length formula is equal to the radius of the circle.

Finding Percentage Difference

Introduction:

            Percentage is expressing any number in a fraction with the denominator as 100. The symbol used for the percentage is ‘%’. Percentage difference is defined as the comparing a previous value to the new value and the percent difference.
Formula for percentage difference Calculator = [Previous value – new value] / 100

Word Problem on Find Percentage Difference:

David lived in a United States of America. When David left the country the population was 920 million. David recently heard that the population has decreased by 6%. What is the present population?
Solution:
Find out the decrease percentage 920*6/100 = 5520/100 = 55.2 million
      Then the new population is old population minus the decreased population
      920-55.2 = 864.8 million
      The population is now 864.8 million

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Explain Statistical Graphical Representation

Introduction on Statistics and Graphical Representation:

           Statistics is about collection of information and its presentation and about drawing inferences from these. We come across facts and figures in the newspapers, Television and the radio. The numerical figures are called "the data". If we have to draw good inferences from information collected, it has to be presented properly.

             The graphical representation of data makes the reading more interesting, less time-consuming and easily understandable. The disadvantage of graphical presentation is that it lacks details and is less accurate. In our study, we have the following graphs: 1. Bar Graphs 2. Pie Charts 3. Frequency Polygon 4. Histogram.

Statistical Graphical Representation:

         The scientific methods of collection of data, its classification and application to commerce and everyday life is called statistics. A list of some important terms as follows: (i) ungrouped data (ii) tabulation of data (iii) range (iv) frequency (v) frequency distribution (vi) tally (vii) inclusive type of grouped frequency distribution (viii) exclusive type of grouped frequency distribution (ix) lower limit and actual lower limit (x) upper limit and actual upper limit (xi) class size or class width (xii) class mark or class mid-interval (xiii) Variables (xiv) Continuous Variables (xv) Discrete Variables.

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