The velocity of pressure waves in a liquid can be determined using the equation:

v = √(E/ρ)

where v is the velocity of the pressure waves, E is the bulk modulus of the liquid, and ρ is the density of the liquid.

Explanation:

1. Introduction to Pressure Waves:
Pressure waves are disturbances that propagate through a medium, causing variations in pressure. In a liquid, these waves travel as longitudinal waves, where the particles of the liquid oscillate parallel to the direction of wave propagation.

2. Relationship between Velocity and Bulk Modulus:
The velocity of pressure waves in a medium is directly related to the bulk modulus of the medium. The bulk modulus is a measure of a material's resistance to compression. In other words, it quantifies how easily a material can be compressed or how much it resists changes in volume under pressure.

3. Equation for Velocity of Pressure Waves:
The equation v = √(E/ρ) relates the velocity of pressure waves to the bulk modulus and density of the liquid. Taking the square root of the ratio of bulk modulus to density gives the velocity of the waves.

4. Explanation of the Options:
a) (E/)^(1/2):
This option correctly represents the equation for the velocity of pressure waves. The square root of the ratio of the bulk modulus E to the density ρ is taken.

b) (E)^(1/2):
This option is incorrect as it only takes the square root of the bulk modulus E, without considering the density ρ.

c) (/E):
This option is incorrect as it takes the ratio of the density ρ to the bulk modulus E, without considering the square root.

d) (1/E)^(1/2):
This option is incorrect as it takes the square root of the reciprocal of the bulk modulus E, without considering the density ρ.

5. Conclusion:
The correct answer is option 'A' (E/)^(1/2), as it represents the correct equation for the velocity of pressure waves in a liquid. The velocity is determined by taking the square root of the ratio of the bulk modulus E to the density ρ.