rationalize the denominater 7+ 3square root of 5  divided by 7-  3square root of 5

Asked by kaushik3199 | 26th May, 2021, 03:45: PM

Expert Answer:

begin mathsize 16px style fraction numerator 7 plus 3 square root of 5 over denominator 7 minus 3 square root of 5 end fraction
Rationalizing space the space denominator
equals fraction numerator 7 plus 3 square root of 5 over denominator 7 minus 3 square root of 5 end fraction cross times fraction numerator 7 plus 3 square root of 5 over denominator 7 plus 3 square root of 5 end fraction
equals fraction numerator open parentheses 7 plus 3 square root of 5 close parentheses open parentheses 7 plus 3 square root of 5 close parentheses over denominator open parentheses 7 minus 3 square root of 5 close parentheses open parentheses 7 plus 3 square root of 5 close parentheses end fraction
equals fraction numerator open parentheses 7 plus 3 square root of 5 close parentheses squared over denominator open parentheses 7 close parentheses squared minus open parentheses 3 square root of 5 close parentheses squared end fraction space space space space........ space left parenthesis straight a space minus space straight b right parenthesis left parenthesis straight a space plus space straight b right parenthesis space equals space straight a squared minus space straight b squared
equals fraction numerator 49 space plus space 42 square root of 5 space plus space 45 over denominator 49 space minus space 45 end fraction space space space space space space space space space............. space left parenthesis straight a space plus space straight b right parenthesis squared space equals space straight a to the power of 2 end exponent plus 2 ab space plus space straight b squared
equals fraction numerator 94 plus space 42 square root of 5 over denominator 4 end fraction
equals fraction numerator 2 open parentheses 47 plus 21 square root of 5 close parentheses over denominator 4 end fraction
equals fraction numerator 47 plus 21 square root of 5 over denominator 2 end fraction
end style

Answered by Yasmeen Khan | 28th May, 2021, 12:09: AM