Question 213597
sqrt (2/3),,,,,,,sqrt (3/4)
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to  simplify (reduce)  we  factor,  but  with  perfect  squares(1,4,9,16,25,36,49,etc)
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Let's  do    sqrt (3/4)  first,,,
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This  also  equals ,,,,(sqrt 3)/ (sqrt 4),,,,
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the  sqrt  of  3  has  only  1 as  a potential  factor,  and  this  does not  help

The sqrt  of  4  has  4  as  a  perfect  square (2*2),  and  can  be  simplified
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To  (sqrt 3)/ (2),,,  (just  2,,  no  sqrt),,,so
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sqrt(3/4) = (sqrt 3) /2 = (1/2) sqrt 3
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checking  with  a  calc,  sqrt(3/4) = .866,,,,1/2 sqrt3=.866,,,,ok
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Returning  to  sqrt(2/3),   there  are  no  perfect  square  factors  that  will  help,  so  this  is  in  simplified  form already.
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sqrt(2/3) = sqrt .667 = .816
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a  Better  example  might  be  sqrt50 = sqrt(25*2)= sqrt25 * sqrt2= 5sqrt2
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or  sqrt 200 = sqrt(100*2) = sqrt(100) * sqrt2 = 10sqrt2
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