Where from the root 3 in this power Eq. Power = root 3.V.I.pf.

root 3 is used in order to use voltage line to line instead of line to neutral voltages.

You can check at "section 2.6 from power system analisys and design by J. Duncan Glober and sarma"

I need to say that I agree in completely with sir Enrique in aspect of his explanation of meaning of "sqrt 3" except I would like to add that value of line voltage is (sqrt(3)) times higher than value of phase voltage and I would like to add that phasor of line voltage leads in front of appropriate phasor of phase voltage which means that angle of line voltage is higher than angle of phase voltage for 30 degree.
I think that is the best option, which I would like to suggest to our colleague, is to draw diagram of symmetric order of phasors of voltages (their phasors are shifted for 120 degree in the space) and then, at the same diagram, to draw phasors of line voltages, so, as he could to compare their values and angles and to easier understand behaving of phase voltages and line voltages in AC three phase power system.

You right Mr. Bojan...thanks for the additional explanation.

Regards

Three phase power is actually 3 x single phase power. Single phase power is Vph x Iph x pf. So, three phase power is: 3 x Vph x Iph x pf.

In star connected networks, Vph = VL/Root 3 and Iph = IL. Thus, three phase power in a star connected network is: 3 x (VL / Root 3) x IL x pf (i.e.) Root 3 x VL x IL x pf.

Similarly, in a delta connected network, Vph = VL & Iph = IL/Root 3. Thus, three phase power in a delta connected network is: 3 x VL x (IL/Root 3) x pf (i.e.) Root 3 x VL x IL x pf.

Hope it is clear.

Dear Edem, as you aware V / I in AC are vectors ie they are of magnitude and direction (angle).
Therefore, in Star, 4 Wire (R,Y,B & N) was found that line voltage between R & Y is equal the sum of Vector phase voltage between R & N plus Y&N.
By mathmatical calculation (phasor)

V(RN) + V(YN) = VRY (Vectors)
V-phase as magnitude = root(3) V-line
ie magnitudes of V-phase=VRN=VYN= Root(3) V-line, and I-line = I-phase)
For delta:
I-line =Root (3) I-Phase
V-line = V-phase

Based on the above
The power in 3-phase P is
P= V-line X I-line X P.f ( Cos(phi)), phi the angle between V & I.

Since either I-line = I-phase or V-line = V-phase, not both ( depends on the connection, is it Delta or Star)
then
P = root(3) VI. p.f

By other way and further to Mr.Sivakumar comments:
Power in 3-phase = 3 X power per phase
P = 3V-phaes X I-phase X p.f

either V-phase = V-line or I-phase = I-line not both.

Then
P= 3 V-line X I-line/(root3) X p.f
= Root(3) VI.p.f

Every comment is given me more n more understand thank 2 u all.