Rationalize the denominator of:

1 ÷ 3 - 2×under root 2 + under root 5

Asked by bhengraj68 | 17th May, 2019, 01:52: PM

Expert Answer:

begin mathsize 16px style fraction numerator 1 over denominator 3 space minus space 2 square root of 2 space space plus space square root of 5 end fraction
equals space fraction numerator 1 over denominator open parentheses 3 space minus space 2 square root of 2 close parentheses space space plus space open parentheses square root of 5 close parentheses end fraction cross times space fraction numerator open parentheses 3 space minus space 2 square root of 2 close parentheses space space minus space open parentheses square root of 5 close parentheses over denominator open parentheses 3 space minus space 2 square root of 2 close parentheses space space minus space open parentheses square root of 5 close parentheses end fraction
equals space fraction numerator open parentheses 3 space minus space 2 square root of 2 close parentheses space space minus space open parentheses square root of 5 close parentheses over denominator open parentheses 3 space minus space 2 square root of 2 close parentheses squared space minus space open parentheses square root of 5 close parentheses squared end fraction
equals space fraction numerator open parentheses 3 space minus space 2 square root of 2 close parentheses space space minus space open parentheses square root of 5 close parentheses over denominator 9 space space minus space 12 square root of 2 space plus space 8 space minus space 5 end fraction
equals fraction numerator 3 space minus space 2 square root of 2 space minus square root of 5 space over denominator 12 space minus space 12 square root of 2 end fraction
equals space fraction numerator 3 space minus space 2 square root of 2 space minus square root of 5 over denominator 12 open parentheses 1 space minus space square root of 12 close parentheses end fraction space cross times space fraction numerator 1 space plus space square root of 12 over denominator 1 space plus space square root of 12 end fraction
equals fraction numerator open parentheses 3 space minus space 2 square root of 2 space minus square root of 5 close parentheses open parentheses 1 space plus space square root of 12 close parentheses over denominator 12 left parenthesis 1 space minus space 12 right parenthesis end fraction
equals fraction numerator open parentheses 3 space minus space 2 square root of 2 space minus square root of 5 close parentheses open parentheses 1 space plus space square root of 12 close parentheses over denominator negative 132 end fraction end style

Answered by Yasmeen Khan | 17th May, 2019, 02:50: PM