### Related

##### sqrt

U1:sqrt(sqrt(4*M/n^2));

U2:2*sqrt(1/(2*n)*sqr...

b:simplify(U1-U2);

Calculate

##### sqrt

sqrt( (2*(x*x))-(2*x) );

Calculate

a:7;

b:8;

sqrt(a^2+b^2);

Calculate

##### sqrt

e:10*10^-10 = ((12*1....

esolve([e],[R]);

R=sqrt(1000000000*3.6...

Calculate

u:[1,4,3];

v:[1,-2,4];

u*v;

Calculate

##### sqrt

uv:[2,1,0].[3,-1,2];

uw:[2,1,0].[4,0,3];

vw:[3,-1,2].[4,0,3];

Calculate

##### sqrt

(62500000*sqrt(991877...

Calculate

##### sqrt

(0.5+sqrt(1-(1/2)^2)/...

Calculate

##### sqrt

f(x):=(sqrt(x^2+4)-2)/x;

f(0.5);

f(0.3);

Calculate

a1:0.2;

h:0.0002 ;

S:950;

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
```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) ```
Run Example
```x:0.25;
(%o1)                                0.25
(%i2) Fs:0.7;
(%o2)                                 0.7
(%i3) Pv:0.41;
(%o3)                                0.41
(%i4) solve(  Fs = sqrt(1/(1+Pv*(1/((F0*(1-sqrt(x) ) + sqrt(x) )^2)  -1 ))),F0),numer;

rat: replaced 0.7 by 7/10 = 0.7

rat: replaced 0.41 by 41/100 = 0.41

rat: replaced 0.5 by 1/2 = 0.5

rat: replaced 0.5 by 1/2 = 0.5

rat: replaced -0.5 by -1/2 = -0.5

rat: replaced 0.7 by 7/10 = 0.7

rat: replaced -0.1 by -1/10 = -0.1

rat: replaced 0.41 by 41/100 = 0.41

rat: replaced 0.5 by 1/2 = 0.5

rat: replaced 0.5 by 1/2 = 0.5

rat: replaced -0.5 by -1/2 = -0.5

rat: replaced 0.41 by 41/100 = 0.41

rat: replaced 0.5 by 1/2 = 0.5

rat: replaced 0.5 by 1/2 = 0.5

rat: replaced -0.5 by -1/2 = -0.5

rat: replaced 0.41 by 41/100 = 0.41

rat: replaced 0.5 by 1/2 = 0.5

rat: replaced 0.5 by 1/2 = 0.5

rat: replaced -0.5 by -1/2 = -0.5

rat: replaced -2.04081632653061 by -100/49 = -2.04081632653061

rat: replaced -2.04081632653061 by -100/49 = -2.04081632653061

rat: replaced -2.040816326530612E-4 by -1/4900 = -2.040816326530612E-4

rat: replaced 15116.60332217526 by 876763/58 = 15116.60344827586

rat: replaced 15116.60332217526 by 876763/58 = 15116.60344827586
(%o4)         [F0 = - 2.063201817996614, F0 = 0.063201817996614]
(%i5) F00:0.063202;
(%o5)                              0.063202
(%i6) y:0;
(%o6)                                  0
(%i7) sqrt(    1/    (1+Pv*(    1/( (F00*(1-sqrt(y) )+sqrt(y))^2)   -1 ) )      ) ,numer;
(%o7)                          0.098422471651816
(%i8) y:x;
(%o8)                                0.25
(%i9) sqrt(    1/    (1+Pv*(    1/( (F00*(1-sqrt(y))+sqrt(y))^2)   -1 ) )      ) ,numer;
(%o9)                          0.70000008933756
(%i10) y:1;
(%o10)                                 1
(%i11) sqrt(    1/    (1+Pv*(    1/( (F00*(1-sqrt(y))+sqrt(y))^2)   -1 ) )      ) ,numer;
(%o11)                                1.0
(%i12) (sqrt(Pv/(1/Fs^2 -1+Pv))-sqrt(x))/(1-sqrt(x));
(%o12)                         0.063201809127532
(%i13) F: F00*(1-sqrt(x))+ sqrt(x);
(%o13)                             0.531601
(%i14) sqrt(    1/    (1+Pv*(    1/( F)^2   -1 ) )      ) ,numer;
(%o14)                         0.70000008933756
(%i15) ```

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