R a t i o n a l i s e space semicolon space
fraction numerator 4 square root of 3 plus 5 square root of 2 over denominator square root of 48 plus square root of 18 end fraction

Asked by kishor.kp14 | 20th Jun, 2019, 10:18: AM

Expert Answer:

begin mathsize 16px style fraction numerator 4 square root of 3 space plus space 5 square root of 2 over denominator square root of 48 space plus space square root of 18 end fraction
equals space fraction numerator begin display style 4 square root of 3 space plus space 5 square root of 2 end style over denominator begin display style square root of 48 space plus space square root of 18 end style end fraction space cross times space fraction numerator square root of 48 space minus space square root of 18 over denominator square root of 48 space minus space square root of 18 end fraction
equals fraction numerator open parentheses 4 square root of 3 space plus space 5 square root of 2 close parentheses begin display style open parentheses square root of 48 space minus space square root of 18 close parentheses end style over denominator 48 space minus space 18 end fraction space space..... space since space straight a squared space minus space straight b squared space equals space open parentheses straight a space minus space straight b close parentheses open parentheses straight a space plus space straight b close parentheses
equals fraction numerator begin display style open parentheses 4 square root of 3 space plus space 5 square root of 2 close parentheses open parentheses 4 square root of 3 space minus space 3 square root of 2 close parentheses end style over denominator 48 space minus space 18 end fraction
equals space fraction numerator open parentheses 16 space cross times space 3 close parentheses begin display style space end style begin display style minus end style begin display style space end style begin display style 12 end style begin display style square root of 6 end style begin display style space end style begin display style plus end style begin display style space end style begin display style 20 end style begin display style square root of 6 end style begin display style space end style begin display style minus end style begin display style space end style begin display style open parentheses 15 space cross times space 2 close parentheses end style over denominator 30 end fraction
equals space fraction numerator 48 space minus space 30 space plus space 38 square root of 6 over denominator 30 end fraction
equals space fraction numerator 18 space plus space 38 square root of 6 over denominator 30 end fraction
equals space fraction numerator 9 space plus space 19 square root of 6 over denominator 15 end fraction end style

Answered by Yasmeen Khan | 20th Jun, 2019, 10:36: AM