Rationalize:-1/(wholeroot8+root3) or 1/whole√(8+√3) both are same.Please solve it its urgent.

Asked by Harsh | 4th Dec, 2017, 03:39: PM

Expert Answer:

If your question is
fraction numerator 1 over denominator square root of left parenthesis 8 plus square root of 3 right parenthesis end root end root end fraction
 
On Simplifying,
 
 
fraction numerator 1 over denominator square root of left parenthesis 8 plus square root of 3 right parenthesis end root end root end fraction cross times fraction numerator square root of left parenthesis 8 plus square root of 3 right parenthesis end root end root over denominator square root of left parenthesis 8 plus square root of 3 right parenthesis end root end root end fraction
equals fraction numerator square root of left parenthesis 8 plus square root of 3 right parenthesis end root end root over denominator 8 plus square root of 3 end fraction
 
 
Think of what could be the rationalizing factor (RF), here. It is,
square root of 8 minus square root of 3
 
On rationalization, we get,
fraction numerator square root of left parenthesis 8 plus square root of 3 right parenthesis end root end root over denominator square root of 8 plus square root of 3 end fraction cross times fraction numerator square root of 8 begin display style minus end style begin display style square root of 3 end style over denominator square root of 8 begin display style minus end style begin display style square root of 3 end style end fraction

equals space fraction numerator square root of 8 begin display style minus end style begin display style square root of 3 end style over denominator 8 minus 3 end fraction cross times square root of left parenthesis 8 plus square root of 3 right parenthesis end root end root
equals space fraction numerator begin display style square root of 8 minus square root of 3 end style over denominator 5 end fraction cross times square root of left parenthesis 8 plus square root of 3 right parenthesis end root end root
 

Answered by  | 4th Dec, 2017, 05:29: PM

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