Express with rational denominator

15/√10+√20+√40-whole under root5-√80

Asked by karanbora625 | 29th Oct, 2019, 12:05: PM

Expert Answer:

begin mathsize 16px style fraction numerator 15 over denominator square root of 10 space plus space square root of 20 space plus space square root of 40 space minus space square root of 5 space minus space square root of 80 end fraction
equals space fraction numerator 15 over denominator square root of 10 space plus space 2 square root of 5 space plus space 2 square root of 10 space minus space square root of 5 space minus space 4 square root of 5 end fraction
equals space fraction numerator 15 over denominator square root of 10 space plus space 2 square root of 5 space plus space 2 square root of 10 space minus space square root of 5 space minus space 4 square root of 5 end fraction
equals space fraction numerator 15 over denominator 3 square root of 10 space minus space 3 square root of 5 end fraction
equals space fraction numerator 5 over denominator square root of 10 space minus space square root of 5 end fraction
equals fraction numerator 5 over denominator square root of 10 space minus space square root of 5 end fraction cross times fraction numerator square root of 10 space plus space square root of 5 over denominator square root of 10 space plus space square root of 5 end fraction
equals fraction numerator 5 open parentheses square root of 10 space plus space square root of 5 close parentheses over denominator 10 space minus space 5 end fraction equals space square root of 10 space plus space square root of 5 end style

Answered by Yasmeen Khan | 30th Oct, 2019, 10:55: AM