Rationalize: 

5 root 3 - root 2 / 5 root 6 - 2 root 3

Asked by rnagarajan31 | 12th Aug, 2019, 12:34: PM

Expert Answer:

begin mathsize 16px style fraction numerator 5 square root of 3 minus square root of 2 over denominator 5 square root of 6 minus 2 square root of 3 end fraction end style
begin mathsize 16px style equals fraction numerator 5 square root of 3 minus square root of 2 over denominator 5 square root of 6 minus 2 square root of 3 end fraction cross times fraction numerator 5 square root of 6 plus 2 square root of 3 over denominator 5 square root of 6 plus 2 square root of 3 end fraction end style
begin mathsize 16px style equals fraction numerator 25 square root of 3 square root of 6 plus 10 square root of 3 cross times square root of 3 minus 5 square root of 2 square root of 6 minus 2 square root of 2 square root of 3 over denominator 5 squared cross times 6 minus 2 squared cross times 3 end fraction
end style
begin mathsize 16px style equals fraction numerator 25 cross times 3 cross times square root of 2 plus 30 minus 5 cross times 2 cross times square root of 3 minus 2 square root of 6 over denominator 150 minus 12 end fraction end style
begin mathsize 16px style equals fraction numerator 75 square root of 2 plus 30 minus 10 square root of 3 minus 2 square root of 6 over denominator 138 end fraction end style

Answered by Sneha shidid | 13th Aug, 2019, 09:56: AM