Rationalizing the Denominator

Previously we have discussed about adding scientific notation calculator and In today's session we are going to discuss about Rationalizing the Denominator which comes under andhra pradesh state board of secondary education,  The process of eliminating a square root or imaginary number from the denominator of a fraction is termed as rationalization. A rational number is a number that can be expressed as the ratio of two integers, such as 2/3. Any number with a terminating decimal part is a rational number. If decimal part begins to repeat in a numeral, it is also rational number, such as .0303030..., since this can be expressed as 1/33.  Numbers that are not rational are known as irrational.  Examples of irrational numbers are the square root of 2, pi, and e. Examples of rational no are 2/4,3/5.

Rationalizing the Denominator is done to simplifying fractions into simplest form i.e. the denominator should not have an irrational number or a complex number.
In case of real number there are 3 cases where we use rationalization
1. The denominator having single square root
2. The denominator having single higher root
3. The denominator having sums and differences of square roots
case 1:
 When you have a single square root in the denominator you just multiply top and bottom by it.
Example:

1/
=1*/*

=1*/3
in th above example  the denominator is . so we need to rartionaze it forthis we multiply and divide it by the same no . doing this the value of the expression remains same and the square root gets removed from the denominator as * gives 3 which is not irrational

case 2:When we have denominators having higher root
example:   1/

=1/(*)

 = 1/a
since this is a 3rd root, in order to remove the root from the denominator we have to get cube of the values inside the root. To get this we multiply the denominator and numerator with the cube root of the square of the value. Finally we get the cube root of the cube of the value and thus the cube root is removed and we get a rational no in the denominator. (Know more about Rationalizing the Denominator in broad manner, here,)
CASE 3: When the denominator is having   sums and differences of square roots
example:2/1-

=2*(1+)/(1-)(1+)

=2*(1+)/1-3

=2*(1+)/-2

=-(1+)

In this case if a sum is in the denominator we  multiply the denominator and numerator with the difference. And if we have a difference in the denominator we multiply the denominator and numerator with the sum. Thus we rationalize denominator.
In The Next Session We Are Going to Discuss Equations with no Solution

and Read more maths topics of different grades such as Equations and Inequalities in the upcoming sessions here.