Question

please explain why this √3/√2 answer is come.

Answer 1

Formula for the refractive index,
u = sin(i)/sin(r)
where u is the refractive index, i is the angle of incident and r is the angle of refraction.
This is the formula when the ray moves from rarer medium to denser medium.

Now if we look closely, the incident ray is refracted away from the normal. This takes place when the ray moves from a denser to rarer medium.
For the case of denser to rarer, the formula becomes,
u = sin(r)/sin(i)
u = sin60°/sin45°
u = (√3/2)/(1/√2)
u = (√3*√2)/2
u = (√3*√2)/(√2*√2) [2 = √2*√2]
u = √3/√2

And... that's verified.