Soory it was root 32.Please rationalize it. 1/√(8-√32). In words it is 1/wholeroot8-root32.Please solve it is urgent because of exam.Actuly answer given is 1/-√2.Please solve anyhow and fast.

Asked by Harsh | 4th Dec, 2017, 11:48: PM

Expert Answer:

begin mathsize 16px style equals fraction numerator square root of 8 plus square root of 32 end root over denominator square root of 8 minus square root of 32 end root open parentheses square root of 8 plus square root of 32 end root close parentheses end fraction
equals fraction numerator begin display style square root of 8 plus square root of 32 end root end style over denominator begin display style square root of 64 minus 32 end root end style end fraction
equals fraction numerator begin display style square root of 8 plus square root of 32 end root end style over denominator begin display style square root of 32 end style end fraction
equals fraction numerator begin display style 2 square root of 2 plus square root of 2 end root end style over denominator begin display style 4 square root of 2 end style end fraction
equals fraction numerator begin display style square root of 2 plus square root of 2 end root end style over denominator begin display style 2 square root of 2 end style end fraction
equals 1 half square root of fraction numerator 2 plus square root of 2 over denominator 2 end fraction end root
equals fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction square root of 1 plus fraction numerator 1 over denominator square root of 2 end fraction end root
this space is space the space max space simplification space possible end style

Answered by Arun | 5th Dec, 2017, 12:45: PM