Previously we have discussed about area of octagon calculator and In today's session we are going to discuss about Rationalizing the Denominator which comes under andhra pradesh state education board, It defines the method to rewrite a fraction in a form containing merely rational numbers in the denominator. Finding the equivalent expression (which in the denominator not have any radicals) of a radical expression is required in algebra and is known as rationalizing the denominator. In simple words when moving a root value from the bottom of a fraction to the top of fraction is called as rationalizing the denominator . There are basically three types of cases in algebra( check out Algebra Answers for reference) that are:
( a ) square root
( b ) cube root or other roots of higher category
( c ) square root addition or difference
In case ( a ), when in the denominator there is a only single square root then the rationalization process of denominator is done only by multiplying numerator and denominator with the square root. We can understand it by an example as 1 / √ 3 is rationalized by multiplying √ 3 to both numerator and denominator of the fraction. (Know more about in broad manner, here,)
( 1 / √ 3 ) * √ 3 / √ 3 = √ 3 / 3
In case ( b ) when there is higher root (means cube root etc) in the denominator then we multiply and divide the fraction with something that provides the perfect power. For example if there is cube root of 3 in the denominator than we can multiply it by 9 that is the 2nd power of 3 .
We can understand it also by an example as 1 / 3√ p q that is solved as
1 / 3√ p q = 1 / √ p q * 3√ p 2 q 2 / 3√ p 3 q 3 = 3√ p2 q 2/ p q
In case ( c ) numerator and denominator are multiplied with their difference which can be sum or vice versa . To understand it, one example is discussed that is 7 / 9 + √ 10 then
= 7 / 9 + √ 10 * 9 - √ 10 / 9 - √ 10
= 7 ( 9 - √ 10 ) / 81 – 10
= 63 – 7 √ 10 / 71 .
In the next session we are going to discuss about fractional notation calculator
and if anyone want to know about Inequalities then they can refer to Internet and text books for understanding it more precisely.
( a ) square root
( b ) cube root or other roots of higher category
( c ) square root addition or difference
In case ( a ), when in the denominator there is a only single square root then the rationalization process of denominator is done only by multiplying numerator and denominator with the square root. We can understand it by an example as 1 / √ 3 is rationalized by multiplying √ 3 to both numerator and denominator of the fraction. (Know more about in broad manner, here,)
( 1 / √ 3 ) * √ 3 / √ 3 = √ 3 / 3
In case ( b ) when there is higher root (means cube root etc) in the denominator then we multiply and divide the fraction with something that provides the perfect power. For example if there is cube root of 3 in the denominator than we can multiply it by 9 that is the 2nd power of 3 .
We can understand it also by an example as 1 / 3√ p q that is solved as
1 / 3√ p q = 1 / √ p q * 3√ p 2 q 2 / 3√ p 3 q 3 = 3√ p2 q 2/ p q
In case ( c ) numerator and denominator are multiplied with their difference which can be sum or vice versa . To understand it, one example is discussed that is 7 / 9 + √ 10 then
= 7 / 9 + √ 10 * 9 - √ 10 / 9 - √ 10
= 7 ( 9 - √ 10 ) / 81 – 10
= 63 – 7 √ 10 / 71 .
In the next session we are going to discuss about fractional notation calculator
and if anyone want to know about Inequalities then they can refer to Internet and text books for understanding it more precisely.
