Help Me Please.

so the 4root of 100 mutiplied by the sqaure root of 5.

(100)^1/4  / 2 sqrt(5)

(10^2)^1/4 / 2 sqrt5

10^2/4  / 2 sqrt 5

sqrt 10  / 2 sqrt 5

sqrt (5) sqrt (2) / 2 sqrt5

sqrt(2) / 2

.707

⁴√100 /  [2√5]    mutiply top/bottom by  √5

⁴√100 * √5 /  [ 2*√5*√5]  =

⁴√100 * √5  / 10       

Write   ⁴√100   as  ⁴√10^2  =  10^(2/4)  = 10^(1/2) 

And write  √5  =  5^(1/2)

So we have

[ 10^(1/2) * 5^(1/2) ] / 10  =

[  50^(1/2)] / 10 =

√[ 25 * 2 ] / 10  =

5√2 / 10  =

(1/2)√2  =

√2 / 2

Thanks all of You!!