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

Question

2272 views around the world

You can reuse this answer
Creative Commons License

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:
$= (5sqrt6)/6$