`a)`

`5sqrt[1/5]+1/2sqrt20+sqrt5`

`= sqrt[25*1/5]+sqrt[1/4*20]+sqrt5`

`= sqrt5+sqrt5+sqrt5`

`= 3sqrt5`

`b)`

`sqrt[1/2]+sqrt[4.5]+sqrt[12.5]`

`= [sqrt2]/2+[sqrt18]/2+[sqrt50]/2`

`= [sqrt2]/2+[3sqrt2]/2+[5sqrt2]/2`

`= [9sqrt2]/2`

`c)`

`sqrt20-sqrt45+3sqrt18+sqrt72`

`= sqrt[2^2*5]-sqrt[3^2*5]+3sqrt[3^2*2]+sqrt[(2*3)^2 * 2]`

`= 2sqrt5-3sqrt5+9sqrt2+6sqrt2`

`= -sqrt5+15sqrt2`

`d)`

`0.1sqrt200+2sqrt[0.08]+0.4sqrt50`

`= sqrt[0.01*200]+sqrt[4*0.08]+sqrt[0.16*50]`

`= sqrt2+sqrt[0.32]+sqrt8`

`= sqrt2+sqrt[32*0.01]+2sqrt2`

`= sqrt2+0.1*4sqrt2+2sqrt2`

`= 3sqrt2+0.4sqrt2`

`= 3.4sqrt2`

`#2`