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What is the Rationalising factor of 5 1/3 +5 -1/3 find the rationalising factor by prrof

What is the Rationalising factor of 51/3+5-1/3  find the rationalising factor by prrof
 

Grade:9

2 Answers

Arun
25758 Points
2 years ago
Dear student
 
It can be written as 5^1/3 + 5^-1/3
rationalizing factor is ( 5^2/3 + 5 ^-2/3 – 1) as when multiplied, this convert in to the formula of a^3 + b^3
Vikas TU
14149 Points
2 years ago
Dear student 
Here is the explanation of above question.
Your question is how to rationalize the above expression.
The above answer gives you the shortest way to rationalize the expression.
For finding rationalizing factor you can use this method. This is somewhat complex .
Take 5^1/3=a & 5^-1/3=b
Now find the lcm if the exponents.
In this case since the denominator is same therefore the LCM is 3
Now a^3=5 & b^3=5^-1
Since a and b are rational therefore a^3-b^3 is also rational
a^3-b^3=(a-b)(a^2+ab+b^2)
Rationalizing factor of a-b=(5^1/3–5^-1/3)
=5^2/3+5^–2/3+5^2/3*5^-2/3
Now just solve the above expression and get the rationalizing factor
Hope this will help 
Good Luck 

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