The rationalized and simplified form of the expression √(5x)/(2y) is 5x/(2y*√(5x)).
To rationalize the denominator and simplify the expression √(5x)/(2y), we need to eliminate the square root from the denominator. The process involves multiplying the numerator and denominator by a suitable expression that would eliminate the square root in the denominator.
The expression √(5x)/(2y) can be multiplied by √(5x)/√(5x), which is the conjugate of the denominator. The conjugate has the same terms but with the opposite sign between them.
Multiplying the numerators and denominators, we get (sqrt(5x))(√(5x))/(2y)(√(5x)).
This simplifies to 5x/(2y*√(5x)).
Therefore, the expression √(5x)/(2y) can be rationalized and simplified to 5x/(2y*√(5x)).