### Related

##### sqrt

peu(x1,y1,z1,x2,y2,z2...

modulo(x,y,z):=sqrt(p...

P1(x)=[2,1,0].[3,-1,2];

Calculate

##### sqrt

sqrt(18439594365531024);

Calculate

%pi**sqrt(2);

Calculate

sqrt(25325);

Calculate

##### sqrt-taylor

V1 : -k/2 * (a*sqrt((...

taylor(V1, [x,y], 0, 4);

Calculate

##### sqrt

eq1:2.22*10^-2*sqrt((...

Calculate

##### sqrt

a:sqrt(sqrt(5)+3);

b:sqrt(sqrt(5)-2);

x: a+b;

Calculate

##### sqrt

1/(x-y*sqrt(-1))^2;

Calculate

##### sqrt

peu (x1,y1,z1,x2,y2,z...

modulo (x,y,z):= sqrt...

peu(2,1,0,3,-1,2);

Calculate

##### sqrt

peu(x1,y1,z1,x2,y2,z2...

modulo(x,y,z):=sqrt(p...

P1=peu(2,1,0,3,-1,2);

Calculate

### sqrt

Run Example
```(%i1)KILL(ALL);
(%o1)                              KILL(ALL)
(%i2) a1:[33,33,35,36,36,35,36,38,35,33,32,34,36,36,35,35,35,25,25,18,23,27,30,31,27,23,23,24,20,21,21];
(%o2) [33, 33, 35, 36, 36, 35, 36, 38, 35, 33, 32, 34, 36, 36, 35, 35, 35, 25,
25, 18, 23, 27, 30, 31, 27, 23, 23, 24, 20, 21, 21]
(%i3)  n1:31;
(%o3)                                 31
(%i4) a2:[33,28,26,29,30,32,24,24,27,30,31,14,18,23,24,24,25,18,23,27,28,29,31,21,23,24,28,32,32,28,21];
(%o4) [33, 28, 26, 29, 30, 32, 24, 24, 27, 30, 31, 14, 18, 23, 24, 24, 25, 18,
23, 27, 28, 29, 31, 21, 23, 24, 28, 32, 32, 28, 21]
(%i5)  n2:31;
(%o5)                                 31
(%i6) a1_sr:(a1[1]+a1[2]+a1[3]+a1[4]+a1[5]+a1[6]+a1[7]+a1[8]+a1[9]+a1[10]+a1[11]+a1[12]+a1[13]+a1[14]+a1[15]+a1[16]+a1[17]+a1[18]+a1[19]+a1[20]+a1[21]+a1[22]+a1[23]+a1[24]+a1[25]+a1[26]+a1[27]+a1[28]+a1[29]+a1[30]+a1[31])/n1,numer;
(%o6)                          30.03225806451613
(%i7) a1_sr_kv:(a1[1]**2+a1[2]**2+a1[3]**2+a1[4]**2+a1[5]**2+a1[6]**2+a1[7]**2+a1[8]**2+a1[9]**2+a1[10]**2+a1[11]**2+a1[12]**2+a1[13]**2+a1[14]**2+a1[15]**2+a1[16]**2+a1[17]**2+a1[18]**2+a1[19]**2+a1[20]**2+a1[21]**2+a1[22]**2+a1[23]**2+a1[24]**2+a1[25]**2+a1[26]**2+a1[27]**2+a1[28]**2+a1[29]**2+a1[30]**2+a1[31]**2)/n1,numer;
(%o7)                          937.3870967741935
(%i8) Disp1:a1_sr_kv-a1_sr**2;
(%o8)                          35.45057232049953
(%i9) sigm1:sqrt(Disp1);
(%o9)                          5.954038320375469
(%i10) a2_sr:(a2[1]+a2[2]+a2[3]+a2[4]+a2[5]+a2[6]+a2[7]+a2[8]+a2[9]+a2[10]+a2[11]+a2[12]+a2[13]+a2[14]+a2[15]+a2[16]+a2[17]+a2[18]+a2[19]+a2[20]+a2[21]+a2[22]+a2[23]+a2[24]+a2[25]+a2[26]+a2[27]+a2[28]+a2[29]+a2[30]+a2[31])/n1,numer;
(%o10)                         26.03225806451613
(%i11) a2_sr_kv:(a2[1]**2+a2[2]**2+a2[3]**2+a2[4]**2+a2[5]**2+a2[6]**2+a2[7]**2+a2[8]**2+a2[9]**2+a2[10]**2+a2[11]**2+a2[12]**2+a2[13]**2+a2[14]**2+a2[15]**2+a2[16]**2+a2[17]**2+a2[18]**2+a2[19]**2+a2[20]**2+a2[21]**2+a2[22]**2+a2[23]**2+a2[24]**2+a2[25]**2+a2[26]**2+a2[27]**2+a2[28]**2+a2[29]**2+a2[30]**2+a2[31]**2)/n1,numer;
(%o11)                         698.483870967742
(%i12) Disp2:a2_sr_kv-a2_sr**2;
(%o12)                         20.80541103017697
(%i13) sigm2:sqrt(Disp2);
(%o13)                         4.561294885246619
(%i14) Disp_VGS:(Disp1*n1+Disp2*n2)/(n1+n2);
(%o14)                         28.12799167533825
(%i15) a_sr_all:(a1_sr*n1+a2_sr*n2)/(n1+n2);
(%o15)                         28.03225806451613
(%i16) Disp_obs:(a1_sr_kv*n1+a2_sr_kv*n2)/(n1+n2)-a_sr_all**2;
(%o16)                         32.12799167533819
(%i17) D_mg:(n1*((a_sr_all-a1_sr)**2)+n2*((a_sr_all-a2_sr)**2))/(n1+n2);
(%o17)                                4.0
(%i18) D_all:Disp_VGS+D_mg;
(%o18)                         32.12799167533825
(%i19) EKO:sqrt(D_mg/D_all);
(%o19)                         0.35284844379917
(%i20) ```
Run Example
```eq0: Rs*Xc1^2/(Rs^2+Xc1^2)=Rl*Xc2^2/(Rl^2+Xc2^2);
2            2
Rs Xc1       Rl Xc2
(%o1)                       ---------- = ----------
2     2      2     2
Xc1  + Rs    Xc2  + Rl
(%i2) eq_Xc1: -Rs*sqrt(Rl*Xc2^2/((Rs*Rl^2)+(Rs-Rl)*Xc2^2));
Rl
(%o2)             - Rs sqrt(-----------------------) abs(Xc2)
2     2
(Rs - Rl) Xc2  + Rl  Rs
(%i3) eq1:(2*Q - Rl/abs(Xc2))^2=Rs^2/eq_Xc1^2;
2     2
Rl    2   (Rs - Rl) Xc2  + Rl  Rs
(%o3)             (2 Q - --------)  = -----------------------
abs(Xc2)                   2
Rl Xc2
(%i4) eq_Xc2: solve(eq1,Xc2);
4 abs(Xc2) Q + Rs - Rl
(%o4) [Xc2 = 0, Xc2 = - Rl sqrt(----------------------),
2
4 Rl Q  - Rs + Rl
4 abs(Xc2) Q + Rs - Rl
Xc2 = Rl sqrt(----------------------)]
2
4 Rl Q  - Rs + Rl
(%i5) ```
Run Example
```Z0: (p1 - p2)/SE;
p1 - p2
(%o1)                               -------
SE
(%i2) Z1 : ratsubst(sqrt(p*(1-p)*((1/n1)+(1/n2))),SE,Z0);
p2 - p1
(%o2)                     - -------------------------
1    1
sqrt((-- + --) (1 - p) p)
n2   n1
(%i3) Z2 : ratsubst((p1*n1+p2*n2)/(n1+n2),p,Z1);
p2 - p1
(%o3) - --------------------------------------------------------------------
2    2                                        2    2
n2  (p2  - p2) + n1 n2 ((2 p1 - 1) p2 - p1) + n1  (p1  - p1)
sqrt(- ------------------------------------------------------------)
2     2
n1 n2  + n1  n2
(%i4) Z3 : ratsubst(x*p2,p1,Z2);
(%o4)
p2 x - p2
-----------------------------------------------------------------------------
2    2  2                 2            2                         2
p2  (n1  x  + 2 n1 n2 x + n2 ) + p2 (- n1  x + n1 n2 (- x - 1) - n2 )
sqrt(- ---------------------------------------------------------------------)
2     2
n1 n2  + n1  n2
(%i5) solve(Z3,x);
(%o5)                               [x = 1]
(%i6) ```

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