5 plus 2 square root of 3 divided by 7 plus 4 square root of 3

Asked by sabattanikharbuki | 5th Mar, 2020, 08:25: PM

Expert Answer:

Rationalising the denominator,
 
begin mathsize 16px style fraction numerator 5 plus 2 square root of 3 over denominator 7 plus 4 square root of 3 end fraction cross times fraction numerator 7 plus 4 square root of 3 over denominator 7 plus 4 square root of 3 end fraction
equals space fraction numerator 5 plus 2 square root of 3 over denominator 7 plus 4 square root of 3 end fraction cross times fraction numerator 7 minus 4 square root of 3 over denominator 7 minus 4 square root of 3 end fraction
equals fraction numerator open parentheses 5 plus 2 square root of 3 close parentheses open parentheses 7 minus 4 square root of 3 close parentheses over denominator 49 minus 16 left parenthesis 3 right parenthesis end fraction
equals open parentheses 5 plus 2 square root of 3 close parentheses open parentheses 7 minus 4 square root of 3 close parentheses
equals 35 space minus space 20 square root of 3 space plus space 14 square root of 3 minus 24
equals 11 minus 6 square root of 3 space end style

Answered by Yasmeen Khan | 6th Mar, 2020, 10:28: AM