rationlise denominator of fraction numerator 12 over denominator 3 plus square root of 5 minus 2 end root square root of 2 end fraction

Asked by pvarshithreddy13 | 20th May, 2019, 07:05: AM

Expert Answer:

begin mathsize 16px style fraction numerator 12 over denominator 3 space plus space square root of 5 space minus space 2 square root of 2 end fraction
equals space fraction numerator begin display style 12 end style over denominator begin display style open parentheses 3 space plus space square root of 5 close parentheses space minus space open parentheses 2 square root of 2 close parentheses end style end fraction cross times space fraction numerator open parentheses 3 space plus space square root of 5 close parentheses begin display style plus end style space open parentheses 2 square root of 2 close parentheses over denominator open parentheses 3 space plus space square root of 5 close parentheses space plus space open parentheses 2 square root of 2 close parentheses end fraction
equals space fraction numerator 12 open square brackets open parentheses 3 space plus space square root of 5 close parentheses plus space open parentheses 2 square root of 2 close parentheses close square brackets over denominator begin display style open parentheses 3 space plus space square root of 5 close parentheses squared end style space space minus open parentheses 2 square root of 2 close parentheses squared space space end fraction
equals fraction numerator begin display style 12 open square brackets open parentheses 3 space plus space square root of 5 close parentheses plus space open parentheses 2 square root of 2 close parentheses close square brackets end style over denominator begin display style 9 space plus space 6 square root of 5 space plus space 5 space minus space 8 space space end style end fraction
equals fraction numerator begin display style 12 open square brackets open parentheses 3 space plus space square root of 5 close parentheses plus space open parentheses 2 square root of 2 close parentheses close square brackets end style over denominator begin display style 6 open parentheses 1 space plus space square root of 5 close parentheses space space end style end fraction cross times space fraction numerator open parentheses 1 space minus space square root of 5 close parentheses over denominator open parentheses 1 space minus space square root of 5 close parentheses end fraction
equals space fraction numerator 2 open square brackets open parentheses 3 space plus space square root of 5 close parentheses plus space open parentheses 2 square root of 2 close parentheses close square brackets open parentheses 1 space minus space square root of 5 close parentheses over denominator 1 space minus space 5 end fraction
equals space fraction numerator begin display style 2 open square brackets open parentheses 3 space plus space square root of 5 close parentheses plus space open parentheses 2 square root of 2 close parentheses close square brackets open parentheses 1 space minus space square root of 5 close parentheses end style over denominator begin display style negative 4 end style end fraction
equals negative fraction numerator begin display style open square brackets open parentheses 3 space plus space square root of 5 close parentheses plus space open parentheses 2 square root of 2 close parentheses close square brackets open parentheses 1 space minus space square root of 5 close parentheses end style over denominator begin display style 2 end style end fraction end style

Answered by Yasmeen Khan | 20th May, 2019, 09:45: AM

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