What is Square root of 2/3 + square root of 3/2?

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Answer 1 · 2015-06-15T04:34:45

#sqrt(2/3) + sqrt(3/2)#

Split the fractions:
#= (sqrt2)/(sqrt3) + (sqrt3)/(sqrt2)#

Cross-multiply:
#= (sqrt2)/(sqrt3)*(sqrt2)/(sqrt2) + (sqrt3)/(sqrt2)*(sqrt3)/(sqrt3)#

#= (2)/(sqrt6) + (3)/(sqrt6)#

Add:
#= (5)/(sqrt6)#

Get rid of the radical in the denominator:
#= (5)/(sqrt6)*sqrt6/sqrt6#

Simplify:
#= (5sqrt6)/6#